pax_global_header00006660000000000000000000000064146651260140014517gustar00rootroot0000000000000052 comment=90036084b3cf811a89181d2f8e9da2558a2f6cc3 fuzzy-logic-toolkit-0.6.1/000077500000000000000000000000001466512601400154705ustar00rootroot00000000000000fuzzy-logic-toolkit-0.6.1/CITATION000066400000000000000000000022641466512601400166310ustar00rootroot00000000000000To cite the fuzzy-logic-toolkit in publications, please use: L. Markowsky and B. Segee. "The Octave Fuzzy Logic Toolkit," Proceedings of the 2011 IEEE International Workshop on Open-Source Software for Scientific Computation (OSSC-2011), pp. 118-125, October 2011. L. Markowsky and B. Segee. "Unsupervised Clustering With the Octave Fuzzy Logic Toolkit," Proceedings of the 2013 IEEE 10th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD-2013), pp. 207-212, July 2013. The BibTex entries for LaTex users: @inproceedings{octavefuzzy01, author = "L. Markowsky and B. Segee", title = {{The Octave Fuzzy Logic Toolkit}}, booktitle = "Proceedings of the 2011 IEEE International Workshop on Open-Source Software for Scientific Computation", month = "October", year = 2011, pages = {118--125} } @inproceedings{octavefuzzy02, author = "L. Markowsky and B. Segee", title = {{Unsupervised Clustering With the Octave Fuzzy Logic Toolkit}}, booktitle = "Proceedings of the 2013 IEEE 10th International Conference on Fuzzy Systems and Knowledge Discovery", month = "July", year = 2013, pages = {207--212} } fuzzy-logic-toolkit-0.6.1/COPYING000066400000000000000000001045131466512601400165270ustar00rootroot00000000000000 GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The GNU General Public License is a free, copyleft license for software and other kinds of works. 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Copyright (C) This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . Also add information on how to contact you by electronic and paper mail. If the program does terminal interaction, make it output a short notice like this when it starts in an interactive mode: Copyright (C) This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, your program's commands might be different; for a GUI interface, you would use an "about box". You should also get your employer (if you work as a programmer) or school, if any, to sign a "copyright disclaimer" for the program, if necessary. For more information on this, and how to apply and follow the GNU GPL, see . The GNU General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. But first, please read . fuzzy-logic-toolkit-0.6.1/ChangeLog000066400000000000000000000356651466512601400172610ustar00rootroot000000000000002024-08-31 L. Markowsky * Version 0.6.1 released. * ChangeLog: Updated file. * DESCRIPTION: Updated file. * NEWS: Updated file. * inst/*.m and inst/private/*.m: Improved many comments. * docs/*.html: Updated html documentation. 2024-06-05 L. Markowsky * Version 0.6.0 released. * ChangeLog: Updated file. * DESCRIPTION: Updated file. * NEWS: Updated file. * inst/*.m and inst/private/*.m: Added many built-in self tests, simplified error messages, and made minor improvements to comments. * inst/private/square_distance_matrix.m and inst/private/update_cluster_membership.m: Reimplemented the two private functions. Tested for identical results with previous implementation using an embedded test in each file. * docs/*.html: New directory containing html documentation for each top-level function. 2024-05-16 L. Markowsky * Version 0.5.1 released. * ChangeLog: Updated file. * DESCRIPTION: Updated file. * NEWS: Updated file. 2024-05-12 L. Markowsky * Version 0.5.0 released. * ChangeLog: Updated file. * DESCRIPTION: Updated file. * NEWS: Updated file. * inst/algebraic_sum.m, inst/bounded_difference.m, and inst/bounded_sum.m: Replaced deprecated '.+' and '.-' operators with '+' and '-', respectively. * inst/*.m: Updated copyright notices. * inst/*.fis: Updated copyright notices. * inst/private/*.m: Updated copyright notices. 2021-02-16 L. Markowsky * Version 0.4.6 released. * ChangeLog: Updated file. * DESCRIPTION: Updated file. * NEWS: Updated file. * inst/defuzz.m: Bug #53549 was fixed (parse error in function defuzz.m -- anonymous function body requires only a single expression). * inst/*.m: Updated copyright notices. * inst/*.fis: Updated copyright notices. * inst/private/*.m: Updated copyright notices. 2014-07-01 L. Markowsky * Version 0.4.5 released. * ChangeLog: Updated file. * DESCRIPTION: Updated file. * NEWS: Updated file. * inst/setfis.m: Bug #38018 was fixed (typo in function setfis.m -- wrong function name). 2014-06-26 L. Markowsky * Version 0.4.4 released. * ChangeLog: Updated file. * CITATION: New file. References to two published papers about the fuzzy-logic-toolkit. * DESCRIPTION: Updated file. * NEWS: Updated file. * inst/readfis.m: Modified to workaround change to strsplit beginning in Octave 3.8.0. * inst/evalmf.m: Removed continuation "..." within double quoted string by writing instruction on one line to maintain compatibility with future versions of Octave. * inst/writefis.m: Changed continuation within double quoted string from "..." to "\" to maintain compatibility with future versions of Octave. * inst/*.m: Updated copyright notices. * inst/*.fis: Updated copyright notices. * inst/private/*.m: Updated copyright notices. * Demos tested under: Fedora 20/Octave 3.8.1 * Demos tested under: Fedora 20/Octave 3.8.0 * Demos tested under: Fedora 20/Octave 3.6.4 2012-10-02 L. Markowsky * Version 0.4.2 released. * ChangeLog: Updated file. * DESCRIPTION: Updated file. * NEWS: Updated file. * inst/*.m: Some trivial changes to line length and comments. * inst/fcm.m: Edited to reflect the five renamed private functions. Edited the demos to calculate and print the three cluster validity indices. Edited comment. * inst/gustafson_kessel.m: Edited to reflect the five renamed private functions. Edited the demos to calculate and print the three cluster validity indices. Edited comment. * inst/partition_coeff.m: Demos were merged with the demos in fcm.m and gustafson_kessel.m and then removed. Edited comment. * inst/partition_entropy.m: Demos were merged with the demos in fcm.m and gustafson_kessel.m and then removed. Edited comment. * inst/xie_beni_index.m: Demos were merged with the demos in fcm.m and gustafson_kessel.m and then removed. Edited comment. * inst/private/evalmf_private.m: Edited comment. * inst/private/is_builtin_language.m: Edited comment. * inst/private/fcm_compute_convergence_criterion.m: Edited and renamed compute_cluster_convergence.m. * inst/private/fcm_compute_objective_fcn.m: Edited and renamed compute_cluster_obj_fcn.m. * inst/private/fcm_init_prototype.m: Edited and renamed init_cluster_prototypes.m. * inst/private/fcm_update_cluster_centers.m: Edited and renamed update_cluster_prototypes.m. * inst/private/fcm_update_membership_fcn.m: Edited and renamed update_cluster_membership.m. * inst/private/probor.m: Removed unused private function. * Demos tested under: Fedora 17/Octave 3.6.2 * Demos tested under: Fedora 16/Octave 3.4.3 * Demos tested under: Windows 7/Octave 3.2.4 2012-08-26 L. Markowsky * Version 0.4.1 released. * ChangeLog: Updated file. * COPYING: Replaced GPLv2 with GPLv3 (to fix inconsistency with source files). * DESCRIPTION: Updated file. * INDEX: Updated file. * NEWS: Updated file. * inst/fcm.m: Rewrote and embedded the demos previously contained in fcm_demo_1.m and fcm_demo_2.m. * inst/fcm_demo_1.m: Removed script file. * inst/fcm_demo_2.m: Removed script file. * inst/gustafson_kessel.m: Rewrote and embedded the demos previously contained in gustafson_kessel_demo_1.m and gustafson_kessel_demo_2.m. * inst/gustafson_kessel_demo_1.m: Removed script file. * inst/gustafson_kessel_demo_2.m: Removed script file. * inst/*.m: Many trivial changes to line length and copyright notices. * inst/private/*.m: Many trivial changes to line length and copyright notice. * All demos tested under: Fedora 17/Octave 3.6.2 2012-07-10 L. Markowsky * Version 0.4.0 released. * ChangeLog: Updated file. * DESCRIPTION: Updated file. * INDEX: Updated file. * NEWS: New file. * inst/fcm.m: New file. Addition of the Fuzzy C-Means clustering algorithm to the toolkit. * inst/fcm_demo_1.m: New file. Addition of demo script. * inst/fcm_demo_2.m: New file. Addition of demo script. * inst/gustafson_kessel.m: New file. Addition of the Gustafson-Kessel clustering algorithm to the toolkit. * inst/gustafson_kessel_demo_1.m: New file. Addition of demo script. * inst/gustafson_kessel_demo_2.m: New file. Addition of demo script. * inst/partition_coeff.m: New file. Addition of a measure of cluster validity. * inst/partition_entropy.m: New file. Addition of a measure of cluster validity. * inst/xie_beni_index.m: New file. Addition of a measure of cluster validity. * inst/private/fcm_compute_convergence_criterion.m: New file. * inst/private/fcm_compute_objective_fcn.m: New file. * inst/private/fcm_init_prototype.m: New file. * inst/private/fcm_update_cluster_centers.m: New file. * inst/private/fcm_update_membership_fcn.m: New file. * inst/private/square_dist_matrix.m: New file. * New demos tested under: Fedora 16/Octave 3.4.3 2011-11-12 L. Markowsky * Version 0.3.0 released. * ChangeLog: Updated file. * DESCRIPTION: Updated file. * inst/*.m: Many trivial changes to comments and spacing in parameter lists. * inst/addrule.m: Edited comment to describe use with hedges. * inst/algebraic_product.m: New file. * inst/algebraic_sum.m: New file. * inst/bounded_difference.m: New file. * inst/bounded_sum.m: New file. * inst/cubic_approx_demo.m: Added plot of output membership functions. * inst/cubic_approximator.fis: Corrected range for FIS output. * inst/drastic_product.m: New file. * inst/drastic_sum.m: New file. * inst/einstein_product.m: New file. * inst/einstein_sum.m: New file. * inst/evalmf.m: Edited to add custom and new built-in hedge support. * inst/hamacher_product.m: New file. * inst/hamacher_sum.m: New file. * inst/heart_disease_demo_1.m : Edited and renamed heart_demo_1.m. Edited script to demonstrate hedges and new T-norm/S-norm pairs. * inst/heart_disease_demo_2.m : Renamed heart_demo_2.m. * inst/investment_portfolio.fis: New file. * inst/investment_portfolio_demo.m: New file. * inst/plotmf.m: Edited to add support for linear output membership functions and to support optional y-limit arguments. * inst/readfis.m: Edited to add custom and built-in hedge support. * inst/showrule.m: Edited to add Chinese, Russian, and Spanish to the built-in languages and to add custom language support. Also edited to add custom hedge support and to implement the hedges "somewhat", "very", "extremely", and "very very". * inst/sugeno_tip_calculator.fis: Edited to demonstrate hedges. * inst/sugeno_tip_demo.m: Edited to demonstrate hedges. * inst/writefis.m: Edited comment to note that zenity is required by the GUI. Code edited to support hedges. * inst/private/*.m: Many trivial changes to spacing in parameter lists. * inst/private/aggregate_output_mamdani.m: Edited to support new built-in T-norm/S-norm pairs when used as the FIS aggregation method. * inst/private/eval_firing_strength.m: Edited to support new built-in T-norm/S-norm pairs when used as the FIS 'and' or 'or' method. * inst/private/evalmf_private.m: Edited to evaluate linear membership functions and to add custom and new built-in hedge support. * inst/private/eval_rules_mamdani.m: Edited to add custom and built-in hedge support. * inst/private/eval_rules_sugeno.m: Edited to add custom and built-in hedge support. * inst/private/fuzzify_input.m: Edited to add custom and built-in hedge support. * inst/private/get_mf_index_and_hedge.m: New file to add hedge support. * inst/private/is_real.m: Improved test. * inst/private/is_real_matrix.m: Improved test. * inst/private/is_builtin_language.m: Renamed is_language.m. Edited test to add 'chinese', 'mandarin', 'pinyin', 'russian', 'pycckii', 'russkij', 'spanish', 'french', and 'german' to the strings specifying built-in languages. * Demos tested under: Fedora 15/Octave 3.4.2 * Demos tested under: Windows 7/Octave 3.2.4 2011-09-01 L. Markowsky * Version 0.2.4 released. * ChangeLog: Updated file. * DESCRIPTION: Updated file. * INDEX: Updated file. * inst/*.m: Numerous trivial changes. * inst/addmf_demo.m: Merged into addmf.m as an embedded demo and then removed. * inst/addvar_demo.m: Merged into addvar.m as an embedded demo and then removed. * inst/showrule_demo.m: Merged into showrule.m as four embedded demos and then removed. * inst/gensurf.m: Edited to permit scalar grids argument. * inst/getfis.m: Edited to implement "version" field in the FIS. * inst/newfis.m: Edited to implement "version" field in the FIS. * inst/readfis.m: Edited to implement "version" field in the FIS and to handle comments, whitespace, and variable number of membership function parameters. * inst/setfis.m: Edited to implement "version" field in the FIS. Fixed several bugs. * inst/writefis.m: Edited to implement "version" field in the FIS. * inst/cubic_approximator.fis: Renamed cubic-approximator.fis. * inst/heart_disease_risk.fis: Renamed heart-disease-risk.fis. Added comments and whitespace. * inst/linear_tip_calculator.fis: Renamed linear-tip-calculator.fis. * inst/mamdani_tip_calculator.fis: Renamed mamdani-tip-calculator.fis and edited to have multiple outputs. * inst/mamdani_tip_demo.m: Edited to demonstrate multiple outputs. * inst/sugeno_tip_calculator.fis: Renamed sugeno-tip-calculator.fis and edited to have multiple outputs. * inst/sugeno_tip_demo.m: Edited to demonstrate multiple outputs. * inst/private/defuzzify_output_mamdani.m: Bug fix (to handle an FIS with multiple outputs). * inst/private/defuzzify_output_sugeno.m: Bug fix (to handle an FIS with multiple outputs). * inst/private/eval_firing_strength.m: Bug fix. * inst/private/eval_rules_mamdani.m: Bug fix (to handle an FIS with multiple outputs). * inst/private/eval_rules_sugeno.m: Bug fix (to handle an FIS with multiple outputs). * inst/private/is_grid_spec.m: Edited test to make more efficient. * inst/private/is_real.m: New file. * Demos tested under: Fedora 15/Octave 3.4.2 * Demos tested under: Fedora 15/Octave 3.2.4 * Demos tested under: Windows 7/Octave 3.2.4 2011-07-19 L. Markowsky * Version 0.2.3 released. * ChangeLog: Updated file. * DESCRIPTION: Updated file. * INDEX: Updated file. * inst/*.m: Edited numerous comments and texinfo comment blocks. * inst/private/*.m: Edited numerous comments and texinfo comment blocks. * inst/cubic_approx_demo.m: New file. * inst/cubic-approximator.fis: New file. * inst/linear-tip-calculator.fis: New file. * inst/linear_tip_demo.m: New file. * inst/heart_demo_1.m: Renamed commandline_demo.m. * inst/heart_demo_2.m: Renamed heart_demo.m. * inst/mamdani_tip_demo.m: Renamed mamdani_demo.m. * inst/sugeno_tip_demo.m: Renamed tipping_demo.m. * inst/gensurf.m: Edited to handle 2-dimensional plots. * inst/private/eval_rules_sugeno.m: Edited to handle linear output membership functions. * Demos tested under: Fedora 15/Octave 3.4.0 * Demos tested under: Fedora 15/Octave 3.2.4 2011-06-21 L. Markowsky * Version 0.2.2 released. * ChangeLog: New file. * DESCRIPTION: Updated file. * inst/addmf.m: Modified to workaround a bug in Octave 3.4.0. * inst/addrule.m: Modified to workaround a bug in Octave 3.4.0. * inst/addvar.m: Modified to workaround a bug in Octave 3.4.0. * inst/gaussmf.m: Modified demo and texinfo comment string. * inst/getfis.m: Modified to workaround a bug in Octave 3.4.0. * inst/readfis.m: Modified to workaround a bug in Octave 3.4.0. * inst/private/aggregate_output_mamdani.m: Modified to workaround a bug in Octave 3.4.0. * inst/private/evalmf_private.m: Modified to workaround a bug in Octave 3.4.0. * Demos tested under: Fedora 15/Octave 3.4.0 * Demos tested under: Fedora 15/Octave 3.2.4 2011-06-08 L. Markowsky * Version 0.2.1 released. * Initial release on Octave-Forge. * Merged membership function demos into related function files. * Created documentation for Octave-Forge website. * DESCRIPTION: Updated file. * Demos tested under: Fedora 13/Octave 3.2.4 2011-05-25 L. Markowsky * Version 0.2 released. * Moved tests/demos/* and tests/fis/* to inst/*. * Changed indentation and spacing to conform to Octave style. * Converted comments to texinfo. * DESCRIPTION: Update file. * Demos tested under: Fedora 13/Octave 3.2.4 2011-04-19 L. Markowsky * Version 0.1 released. * Initial release on SourceForge. * Demos tested under: Fedora 13/Octave 3.2.4 fuzzy-logic-toolkit-0.6.1/DESCRIPTION000066400000000000000000000006021466512601400171740ustar00rootroot00000000000000Name: fuzzy-logic-toolkit Version: 0.6.1 Date: 2024-08-31 Author: L. Markowsky Maintainer: L. Markowsky Title: Octave Fuzzy Logic Toolkit Description: A mostly MATLAB-compatible fuzzy logic toolkit for Octave. Depends: octave (>= 3.2.4) Autoload: no License: GPLv3+ Url: https://github.com/lmarkowsky/fuzzy-logic-toolkit/releases/tag/0.6.1 fuzzy-logic-toolkit-0.6.1/INDEX000066400000000000000000000017111466512601400162620ustar00rootroot00000000000000fuzzy-logic-toolkit >> Octave Fuzzy Logic Toolkit Evaluation defuzz evalfis evalmf Plotting gensurf plotmf File Input/Output of Fuzzy Inference Systems readfis writefis Command-Line Creation and Modification of Fuzzy Inference Systems addmf addrule addvar newfis rmmf rmvar setfis Text Representation of Fuzzy Inference Systems getfis showfis showrule Membership Functions dsigmf gauss2mf gaussmf gbellmf pimf psigmf sigmf smf trapmf trimf zmf T-Norms and S-Norms (in addition to max/min) algebraic_product algebraic_sum bounded_difference bounded_sum drastic_product drastic_sum einstein_product einstein_sum hamacher_product hamacher_sum Complete Fuzzy Inference System Demos cubic_approx_demo heart_disease_demo_1 heart_disease_demo_2 investment_portfolio_demo linear_tip_demo mamdani_tip_demo sugeno_tip_demo Fuzzy Clustering Functions fcm gustafson_kessel partition_coeff partition_entropy xie_beni_index fuzzy-logic-toolkit-0.6.1/Makefile000066400000000000000000000227451466512601400171420ustar00rootroot00000000000000## Copyright 2015-2016 Carnë Draug ## Copyright 2015-2016 Oliver Heimlich ## Copyright 2017 Julien Bect ## Copyright 2017 Olaf Till ## Copyright 2019 John Donoghue ## ## Copying and distribution of this file, with or without modification, ## are permitted in any medium without royalty provided the copyright ## notice and this notice are preserved. This file is offered as-is, ## without any warranty. TOPDIR := $(shell pwd) ## Some basic tools (can be overriden using environment variables) SED ?= sed TAR ?= tar GREP ?= grep CUT ?= cut TR ?= tr TEXI2PDF ?= texi2pdf -q ## Note the use of ':=' (immediate set) and not just '=' (lazy set). ## http://stackoverflow.com/a/448939/1609556 package := $(shell $(GREP) "^Name: " DESCRIPTION | $(CUT) -f2 -d" " | \ $(TR) '[:upper:]' '[:lower:]') version := $(shell $(GREP) "^Version: " DESCRIPTION | $(CUT) -f2 -d" ") ## These are the paths that will be created for the releases. target_dir := target release_dir := $(target_dir)/$(package)-$(version) release_tarball := $(target_dir)/$(package)-$(version).tar.gz html_dir := $(target_dir)/$(package)-html html_tarball := $(target_dir)/$(package)-html.tar.gz ## Using $(realpath ...) avoids problems with symlinks due to bug ## #50994 in Octaves scripts/pkg/private/install.m. But at least the ## release directory above is needed in the relative form, for 'git ## archive --format=tar --prefix=$(release_dir). real_target_dir := $(realpath .)/$(target_dir) installation_dir := $(real_target_dir)/.installation package_list := $(installation_dir)/.octave_packages install_stamp := $(installation_dir)/.install_stamp ## These can be set by environment variables which allow to easily ## test with different Octave versions. ifndef OCTAVE OCTAVE := octave endif OCTAVE := $(OCTAVE) --no-gui --silent --norc MKOCTFILE ?= mkoctfile ## Command used to set permissions before creating tarballs FIX_PERMISSIONS ?= chmod -R a+rX,u+w,go-w,ug-s HG := hg HG_CMD = $(HG) --config alias.$(1)=$(1) --config defaults.$(1)= $(1) HG_ID := $(shell $(call HG_CMD,identify) --id | sed -e 's/+//' ) HG_TIMESTAMP := $(firstword $(shell $(call HG_CMD,log) --rev $(HG_ID) --template '{date|hgdate}')) ## Detect which VCS is used vcs := $(if $(wildcard .hg),hg,$(if $(wildcard .git),git,unknown)) ifeq ($(vcs),hg) release_dir_dep := .hg/dirstate endif ifeq ($(vcs),git) release_dir_dep := .git/index endif TAR_REPRODUCIBLE_OPTIONS := --sort=name --mtime="@$(HG_TIMESTAMP)" --owner=0 --group=0 --numeric-owner TAR_OPTIONS := --format=ustar $(TAR_REPRODUCIBLE_OPTIONS) ## .PHONY indicates targets that are not filenames ## (https://www.gnu.org/software/make/manual/html_node/Phony-Targets.html) .PHONY: help ## make will display the command before runnning them. Use @command ## to not display it (makes specially sense for echo). help: @echo "Targets:" @echo " dist - Create $(release_tarball) for release." @echo " html - Create $(html_tarball) for release." @echo " release - Create both of the above and show md5sums." @echo " install - Install the package in $(installation_dir), where it is not visible in a normal Octave session." @echo " check - Execute package tests." @echo " doctest - Test the help texts with the doctest package." @echo " run - Run Octave with the package installed in $(installation_dir) in the path." @echo " clean - Remove everything made with this Makefile." ## ## Recipes for release tarballs (package + html) ## .PHONY: release dist html clean-tarballs clean-unpacked-release ## To make a release, build the distribution and html tarballs. release: dist html md5sum $(release_tarball) $(html_tarball) @echo "Upload @ https://sourceforge.net/p/octave/package-releases/new/" @echo " and note the changeset the release corresponds to" ## dist and html targets are only PHONY/alias targets to the release ## and html tarballs. dist: $(release_tarball) html: $(html_tarball) ## An implicit rule with a recipe to build the tarballs correctly. %.tar.gz: % $(TAR) -cf - $(TAR_OPTIONS) -C "$(target_dir)/" "$(notdir $<)" | gzip -9n > "$@" clean-tarballs: @echo "## Cleaning release tarballs (package + html)..." -$(RM) $(release_tarball) $(html_tarball) @echo ## Create the unpacked package. ## ## Notes: ## * having ".hg/dirstate" (or ".git/index") as a prerequesite means it is ## only rebuilt if we are at a different commit. ## * the variable RM usually defaults to "rm -f" ## * having this recipe separate from the one that makes the tarball ## makes it easy to have packages in alternative formats (such as zip) ## * note that if a commands needs to be run in a specific directory, ## the command to "cd" needs to be on the same line. Each line restores ## the original working directory. $(release_dir): $(release_dir_dep) -$(RM) -r "$@" ifeq (${vcs},hg) hg archive --exclude ".hg*" --type files "$@" endif ifeq (${vcs},git) git archive --format=tar --prefix="$@/" HEAD | $(TAR) -x $(RM) "$@/.gitignore" endif ## Don't fall back to run the supposed necessary contents of ## 'bootstrap' here. Users are better off if they provide ## 'bootstrap'. 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Maybe useful for testing installation with ## different versions of Octave. install: $(release_tarball) @echo "Installing package under $(installation_dir) ..." $(OCTAVE) --eval $(octave_install_commands) touch $(install_stamp) ## Install only if installation (under target/...) is not current. $(install_stamp): $(release_tarball) @echo "Installing package under $(installation_dir) ..." $(OCTAVE) --eval $(octave_install_commands) touch $(install_stamp) clean-install: @echo "## Cleaning installation under $(installation_dir) ..." -$(RM) -r $(installation_dir) @echo ## ## Recipes for testing purposes ## .PHONY: run doctest check ## Start an Octave session with the package directories on the path for ## interactice test of development sources. run: $(install_stamp) $(run_in_place) --persist ## Test example blocks in the documentation. 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"$<") > "$@" tests: $(TST_SOURCES) fuzzy-logic-toolkit-0.6.1/NEWS000066400000000000000000000075021466512601400161730ustar00rootroot00000000000000Summary of important user-visible changes for fuzzy-logic-toolkit 0.6.1: ------------------------------------------------------------------------ ** Improved many comments and updated the html documentation. Summary of important user-visible changes for fuzzy-logic-toolkit 0.6.0: ------------------------------------------------------------------------ ** Added many built-in self tests, simplified error messages, and made minor improvements to comments. ** Reimplemented two private functions: square_distance_matrix.m and update_cluster_membership.m. Tested for identical results with previous implementation using an embedded test in each file. ** Added new docs directory containing html documentation for each top-level function. Summary of important user-visible changes for fuzzy-logic-toolkit 0.5.1: ------------------------------------------------------------------------ ** Updated several top-level text files (ChangeLog, DESCRIPTION, and NEWS). No change to any code. Summary of important user-visible changes for fuzzy-logic-toolkit 0.5.0: ------------------------------------------------------------------------ ** Replaced several occurrences of the deprecated '.+' and '.-' operators with '+' and '-', respectively. Summary of important user-visible changes for fuzzy-logic-toolkit 0.4.6: ------------------------------------------------------------------------ ** Bug #53549 was fixed (parse error in function defuzz.m -- anonymous function body requires only a single expression). Summary of important user-visible changes for fuzzy-logic-toolkit 0.4.5: ------------------------------------------------------------------------ ** Bug #38018 was fixed (typo in function setfis.m -- wrong function name). Summary of important user-visible changes for fuzzy-logic-toolkit 0.4.4: ------------------------------------------------------------------------ ** The function readfis was modified to workaround the change to strsplit beginning in Octave 3.8.0. Without the modification, readfis will not work with Octave versions >= 3.8.0. The new version of readfis works with all versions of Octave >= 3.2.4 by first checking for the version number of Octave and then selecting either ostrsplit (for Octave >= 3.8.0) or strsplit (for Octave < 3.8.0). ** The files writefis.m and evalmf.m were edited to maintain compatibility with future versions of Octave. Two occurrences of the continuation "..." within double quoted strings in writefis.m were changed to "\". One occurrence of "..." in evalmf.m was removed by writing the instruction on a single line. Summary of important user-visible changes for fuzzy-logic-toolkit 0.4.2: ------------------------------------------------------------------------ ** The demos embedded in partition_coeff.m, partition_entropy.m, and xie_beni_index.m were merged with the embedded demos in fcm.m and gustafson_kessel.m. Summary of important user-visible changes for fuzzy-logic-toolkit 0.4.1: ------------------------------------------------------------------------ ** The package is no longer automatically loaded. ** The following demo scripts were rewritten and embedded in fcm.m, gustafson_kessel.m, partition_coeff.m, partition_entropy.m, and xie_beni_index.m: fcm_demo_1 fcm_demo_2 gustafson_kessel_demo_1 gustafson_kessel_demo_2 (The separate demo script files have been removed.) Summary of important user-visible changes for fuzzy-logic-toolkit 0.4.0: ------------------------------------------------------------------------ ** The following functions are new: fcm gustafson_kessel partition_coeff partition_entropy xie_beni_index ** The following demo scripts are new: fcm_demo_1 fcm_demo_2 gustafson_kessel_demo_1 gustafson_kessel_demo_2 fuzzy-logic-toolkit-0.6.1/docs/000077500000000000000000000000001466512601400164205ustar00rootroot00000000000000fuzzy-logic-toolkit-0.6.1/docs/addmf.html000066400000000000000000000172351466512601400203710ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: addmf

Function Reference: addmf

Function File: fis = addmf (fis, in_or_out, var_index, mf_name, mf_type, mf_params)

Add a membership function to an existing FIS structure and return the updated FIS.

The types/values of the arguments are expected to be:

ArgumentExpected Type or Value
fisan FIS structure
in_or_out’input’ or ’output’ (case-insensitive)
var_indexvalid index of an FIS input/output variable
mf_namea string
mf_typea string
mf_paramsa vector

If mf_type is one of the built-in membership functions, then the number and values of the parameters must satisfy the membership function requirements for the specified mf_type.

Note that addmf will allow the user to add membership functions or membership function names for a given input or output variable that duplicate mfs or mf names already entered.

Also, constant and linear membership functions are not restricted to FIS structure outputs or to Sugeno-type FIS structures, and the result of using them for FIS inputs or Mamdani-type FIS outputs has not yet been tested.

To run the demonstration code, type "demo addmf" (without the quotation marks) at the Octave prompt. This demo creates two FIS input variables and associated membership functions and then produces two figures showing the term sets for the two FIS inputs.

See also: rmmf, setfis

Example: 1

  

 ## Create new FIS.
 a = newfis ('Heart-Disease-Risk', 'sugeno', ...
             'min', 'max', 'min', 'max', 'wtaver');
 
 ## Add two inputs and their membership functions.
 a = addvar (a, 'input', 'LDL-Level', [0 300]);
 a = addmf (a, 'input', 1, 'Low', 'trapmf', [-1 0 90 110]);
 a = addmf (a, 'input', 1, 'Low-Borderline', 'trapmf', ...
            [90 110 120 140]);
 a = addmf (a, 'input', 1, 'Borderline', 'trapmf', ...
            [120 140 150 170]);
 a = addmf (a, 'input', 1, 'High-Borderline', 'trapmf', ...
            [150 170 180 200]);
 a = addmf (a, 'input', 1, 'High', 'trapmf', [180 200 300 301]);
 
 a = addvar (a, 'input', 'HDL-Level', [0 100]);
 a = addmf (a, 'input', 2, 'Low-HDL', 'trapmf', [-1 0 35 45]);
 a = addmf (a, 'input', 2, 'Moderate-HDL', 'trapmf', [35 45 55 65]);
 a = addmf (a, 'input', 2, 'High-HDL', 'trapmf', [55 65 100 101]);
 
 ## Plot the input membership functions.
 plotmf (a, 'input', 1);
 plotmf (a, 'input', 2);

hold is now off for current axes
hold is now off for current axes
plotted figure

plotted figure

fuzzy-logic-toolkit-0.6.1/docs/addrule.html000066400000000000000000000141101466512601400207230ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: addrule

Function Reference: addrule

Function File: fis = addrule (fis, rule_matrix)

Add a list of rules to an existing FIS structure and return the updated FIS.

Each row of the rule_matrix represents one rule and has the form: 

     [in1_mf ... inM_mf out1_mf ... outN_mf weight connect]

where:

Element in Rule VectorExpected Type or Value
in<i>_mfmembership function index for input i
out<j>_mfmembership function index for output j
weightrelative weight of the rule (0 <= weight <= 1)
connectantecedent connective (1 == and; 2 == or)
    
Hedge StringEffect of Applying Hedge
"not"prepend a minus sign to the membership function index
"somewhat"append ".05" to the membership function index
"very"append ".20" to the membership function index
"extremely"append ".30" to the membership function index
"very very"append ".40" to the membership function index
custom hedgeappend .xy, where x.y is the degree to which the membership value should be raised, to the membership function index

To omit an input or output, use 0 for the membership function index. The consequent connective is always "and".

For example, to express: 

     "If (input_1 is mf_2) or (input_3 is not mf_1) or (input_4 is very mf_1),
      then (output_1 is mf_2) and (output_2 is mf_1^0.3)."

with weight 1, the corresponding row of rule_matrix would be: 

     [2   0   -1   4.2   2   1.03   1   2]

For a complete example that uses addrule, see heart_disease_demo_1.m.

See also: heart_disease_demo_1, showrule

fuzzy-logic-toolkit-0.6.1/docs/addvar.html000066400000000000000000000131641466512601400205540ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: addvar

Function Reference: addvar

Function File: fis = addvar (fis, in_or_out, var_name, var_range)

Add an input or output variable to an existing FIS structure and return the updated FIS.

The types/values of the arguments are expected to be:

ArgumentExpected Type or Value
fisan FIS structure
in_or_outeither ’input’ or ’output’ (case-insensitive)
var_namea string
var_rangea vector [x1 x2] of two real numbers

The vector components x1 and x2, which must also satisfy x1 <= x2, specify the lower and upper bounds of the variable’s domain.

To run the demonstration code, type "demo addvar" (without the quotation marks) at the Octave prompt.

Example: 1

  

 a = newfis ('Heart-Disease-Risk', 'sugeno', ...
             'min', 'max', 'min', 'max', 'wtaver');
 a = addvar (a, 'input', 'LDL-Level', [0 300]);
 getfis (a, 'input', 1);

Name = LDL-Level
NumMFs = 0
MFLabels = 
Range = [0 300]
fuzzy-logic-toolkit-0.6.1/docs/algebraic_product.html000066400000000000000000000112201466512601400227530ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: algebraic_product

Function Reference: algebraic_product

Function File: retval = algebraic_product (x)
Function File: retval = algebraic_product (x, y)

Return the algebraic product of the input. The algebraic product of two real scalars x and y is: x * y

For one vector argument, apply the algebraic product to all of elements of the vector. (The algebraic product is associative.) For one two-dimensional matrix argument, return a vector of the algebraic product of each column.

For two vectors or matrices of identical dimensions, or for one scalar and one vector or matrix argument, return the pairwise product.

See also: algebraic_sum, bounded_difference, bounded_sum, drastic_product, drastic_sum, einstein_product, einstein_sum, hamacher_product, hamacher_sum

fuzzy-logic-toolkit-0.6.1/docs/algebraic_sum.html000066400000000000000000000111721466512601400221050ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: algebraic_sum

Function Reference: algebraic_sum

Function File: retval = algebraic_sum (x, y)
Function File: retval = algebraic_sum (x, y)

Return the algebraic sum of the input. The algebraic sum of two real scalars x and y is: x + y - x * y

For one vector argument, apply the algebraic sum to all of elements of the vector. (The algebraic sum is associative.) For one two-dimensional matrix argument, return a vector of the algebraic sum of each column.

For two vectors or matrices of identical dimensions, or for one scalar and one vector or matrix argument, return the pairwise algebraic sum.

See also: algebraic_product, bounded_difference, bounded_sum, drastic_product, drastic_sum, einstein_product, einstein_sum, hamacher_product, hamacher_sum

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Function Reference: bounded_difference

Function File: retval = bounded_difference (x)
Function File: retval = bounded_difference (x, y)

Return the bounded difference of the input. The bounded difference of two real scalars x and y is: max (0, x + y - 1)

For one vector argument, apply the bounded difference to all of the elements of the vector. (The bounded difference is associative.) For one two-dimensional matrix argument, return a vector of the bounded difference of each column.

For two vectors or matrices of identical dimensions, or for one scalar and one vector or matrix argument, return the pairwise bounded difference.

See also: algebraic_product, algebraic_sum, bounded_sum, drastic_product, drastic_sum, einstein_product, einstein_sum, hamacher_product, hamacher_sum

fuzzy-logic-toolkit-0.6.1/docs/bounded_sum.html000066400000000000000000000111631466512601400216140ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: bounded_sum

Function Reference: bounded_sum

Function File: retval = bounded_sum (x)
Function File: retval = bounded_sum (x, y)

Return the bounded sum of the input. The bounded sum of two real scalars x and y is: min (1, x + y)

For one vector argument, apply the bounded sum to all of elements of the vector. (The bounded sum is associative.) For one two-dimensional matrix argument, return a vector of the bounded sum of each column.

For two vectors or matrices of identical dimensions, or for one scalar and one vector or matrix argument, return the pairwise bounded sum.

See also: algebraic_product, algebraic_sum, bounded_difference, drastic_product, drastic_sum, einstein_product, einstein_sum, hamacher_product, hamacher_sum

fuzzy-logic-toolkit-0.6.1/docs/cubic_approx_demo.html000066400000000000000000000104311466512601400227670ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: cubic_approx_demo

Function Reference: cubic_approx_demo

Script File: cubic_approx_demo

Demonstrate the use of the Octave Fuzzy Logic Toolkit to approximate a non-linear function using a Sugeno-type FIS with linear output functions.

The demo:

  • reads an FIS structure from a file
  • plots the input membership functions
  • plots the (linear) output functions
  • plots the FIS output as a function of the input

See also: heart_disease_demo_1, heart_disease_demo_2, investment_portfolio_demo, linear_tip_demo, mamdani_tip_demo, sugeno_tip_demo

fuzzy-logic-toolkit-0.6.1/docs/defuzz.html000066400000000000000000000122421466512601400206160ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: defuzz

Function Reference: defuzz

Function File: crisp_x = defuzz (x, y, defuzz_method)
Function File: crisp_x = defuzz ([x1 x2 ... xn], [y1 y2 ... yn], defuzz_method)

For a given domain, set of fuzzy function values, and defuzzification method, return the defuzzified (crisp) value of the fuzzy function.

The arguments x and y must be either two real numbers or two equal-length, non-empty vectors of reals, with the elements of x strictly increasing. defuzz_method must be a (case-sensitive) string corresponding to a defuzzification method. Defuzz handles both built-in and custom defuzzification methods.

The built-in defuzzification methods are:

MethodValue Returned
centroidReturn the x-value of the centroid.
bisectorReturn the x-value of the vertical bisector of the area.
momReturn the mean x-value of the points with maximum y-values.
somReturn the smallest (absolute) x-value of the points with maximum y-values.
lomReturn the largest (absolute) x-value of the points with maximum y-values.
wtaverReturn the weighted average of the x-values, with the y-values used as weights.
wtsumReturn the weighted sum of the x-values, with the y-values used as weights.
fuzzy-logic-toolkit-0.6.1/docs/drastic_product.html000066400000000000000000000113641466512601400225040ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: drastic_product

Function Reference: drastic_product

Function File: retval = drastic_product (x)
Function File: retval = drastic_product (x, y)

Return the drastic product of the input.

The drastic product of two real scalars x and y is: 

     min (x, y)     if max (x, y) == 1
     0              otherwise

For one vector argument, apply the drastic product to all of the elements of the vector. (The drastic product is associative.) For one two-dimensional matrix argument, return a vector of the drastic product of each column.

For two vectors or matrices of identical dimensions, or for one scalar and one vector or matrix argument, return the pairwise drastic product.

See also: algebraic_product, algebraic_sum, bounded_difference, bounded_sum, drastic_sum, einstein_product, einstein_sum, hamacher_product, hamacher_sum

fuzzy-logic-toolkit-0.6.1/docs/drastic_sum.html000066400000000000000000000113241466512601400216240ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: drastic_sum

Function Reference: drastic_sum

Function File: retval = drastic_sum (x)
Function File: retval = drastic_sum (x, y)

Return the drastic sum of the input.

The drastic sum of two real scalars x and y is: 

     max (x, y)     if min (x, y) == 0
     1              otherwise

For one vector argument, apply the drastic sum to all of the elements of the vector. (The drastic sum is associative.) For one two-dimensional matrix argument, return a vector of the drastic sum of each column.

For two vectors or matrices of identical dimensions, or for one scalar and one vector or matrix argument, return the pairwise drastic sum.

See also: algebraic_product, algebraic_sum, bounded_difference, bounded_sum, drastic_product, einstein_product, einstein_sum, hamacher_product, hamacher_sum

fuzzy-logic-toolkit-0.6.1/docs/dsigmf.html000066400000000000000000000155771466512601400205760ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: dsigmf

Function Reference: dsigmf

Function File: y = dsigmf (x, params)
Function File: y = dsigmf ([x1 x2 ... xn], [a1 c1 a2 c2])

For a given domain x and parameters params (or [a1 c1 a2 c2]), return the corresponding y values for the difference between two sigmoidal membership functions.

The argument x must be a real number or a non-empty list of strictly increasing real numbers, and a1, c1, a2, and c2 must be real numbers. This membership function satisfies the equation: 

     f(x) = 1/(1 + exp(-a1*(x - c1))) - 1/(1 + exp(-a2*(x - c2)))

and in addition, is bounded above and below by 1 and 0 (regardless of the value given by the formula above).

If the parameters a1 and a2 are positive and c1 and c2 are far enough apart with c1 < c2, then: 

      (a1)/4 ~ the rising slope at c1
          c1 ~ the left inflection point
     (-a2)/4 ~ the falling slope at c2
          c2 ~ the right inflection point

and at each inflection point, the value of the function is about 0.5: 

       f(c1) ~ f(c2) ~ 0.5.

Here, the symbol ~ means "approximately equal".

To run the demonstration code, type "demo dsigmf" (without the quotation marks) at the Octave prompt.

See also: gauss2mf, gaussmf, gbellmf, pimf, psigmf, sigmf, smf, trapmf, trimf, zmf

Example: 1

  

 x = 0:100;
 params = [0.5 20 0.3 60];
 y1 = dsigmf(x, params);
 params = [0.3 20 0.2 60];
 y2 = dsigmf(x, params);
 params = [0.2 20 0.1 60];
 y3 = dsigmf(x, params);
 figure('NumberTitle', 'off', 'Name', 'dsigmf demo');
 plot(x, y1, 'r;params = [0.5 20 0.3 60];', 'LineWidth', 2)
 hold on;
 plot(x, y2, 'b;params = [0.3 20 0.2 60];', 'LineWidth', 2)
 hold on;
 plot(x, y3, 'g;params = [0.2 20 0.1 60];', 'LineWidth', 2)
 ylim([-0.1 1.1]);
 xlabel('Crisp Input Value', 'FontWeight', 'bold');
 ylabel('Degree of Membership', 'FontWeight', 'bold');
 grid;
plotted figure

fuzzy-logic-toolkit-0.6.1/docs/einstein_product.html000066400000000000000000000112621466512601400226660ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: einstein_product

Function Reference: einstein_product

Function File: retval = einstein_product (x)
Function File: retval = einstein_product (x, y)

Return the Einstein product of the input. The Einstein product of two real scalars x and y is: (x * y) / (2 - (x + y - x * y))

For one vector argument, apply the Einstein product to all of the elements of the vector. (The Einstein product is associative.) For one two-dimensional matrix argument, return a vector of the Einstein product of each column.

For two vectors or matrices of identical dimensions, or for one scalar and one vector or matrix argument, return the pairwise Einstein product.

See also: algebraic_product, algebraic_sum, bounded_difference, bounded_sum, drastic_product, drastic_sum, einstein_sum, hamacher_product, hamacher_sum

fuzzy-logic-toolkit-0.6.1/docs/einstein_sum.html000066400000000000000000000112071466512601400220110ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: einstein_sum

Function Reference: einstein_sum

Function File: retval = einstein_sum (x)
Function File: retval = einstein_sum (x, y)

Return the Einstein sum of the input. The Einstein sum of two real scalars x and y is: (x + y) / (1 + x * y)

For one vector argument, apply the Einstein sum to all of the elements of the vector. (The Einstein sum is associative.) For one two-dimensional matrix argument, return a vector of the Einstein sum of each column.

For two vectors or matrices of identical dimensions, or for one scalar and one vector or matrix argument, return the pairwise Einstein sum.

See also: algebraic_product, algebraic_sum, bounded_difference, bounded_sum, drastic_product, drastic_sum, einstein_product, hamacher_product, hamacher_sum

fuzzy-logic-toolkit-0.6.1/docs/evalfis.html000066400000000000000000000306451466512601400207470ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: evalfis

Function Reference: evalfis

Function File: output = evalfis (user_input, fis)
Function File: output = evalfis (user_input, fis, num_points)
Function File: [output, rule_input, rule_output, fuzzy_output] = evalfis (user_input, fis)
Function File: [output, rule_input, rule_output, fuzzy_output] = evalfis (user_input, fis, num_points)

Return the crisp output(s) of an FIS for each row in a matrix of crisp input values. Also, for the last row of user_input, return the intermediate results:

Intermediate ResultValue Returned
rule_inputa matrix of the degree to which each FIS rule matches each FIS input variable
rule_outputa matrix of the fuzzy output for each (rule, FIS output) pair
fuzzy_outputa matrix of the aggregated output for each FIS output variable

The optional argument num_points specifies the number of points over which to evaluate the fuzzy values. The default value of num_points is 101.

Argument user_input: user_input is a matrix of crisp input values. Each row represents one set of crisp FIS input values. For an FIS that has N inputs, an input matrix of z sets of input values will have the form: 

   [[input_11 input_12 ... input_1N]   <-- 1st row is 1st set of inputs
    [input_21 input_22 ... input_2N]   <-- 2nd row is 2nd set of inputs
    [             ...              ]                  ...
    [input_z1 input_z2 ... input_zN]]  <-- zth row is zth set of inputs

Return value output: output is a matrix of crisp output values. Each row represents the set of crisp FIS output values for the corresponding row of user_input. For an FIS that has M outputs, an output matrix corresponding to the preceding input matrix will have the form: 

   [[output_11 output_12 ... output_1M]   <-- 1st row is 1st set of outputs
    [output_21 output_22 ... output_2M]   <-- 2nd row is 2nd set of outputs
    [               ...               ]                  ...
    [output_z1 output_z2 ... output_zM]]  <-- zth row is zth set of outputs

The intermediate result rule_input: The matching degree for each (rule, input value) pair is specified by the rule_input matrix. For an FIS that has Q rules and N input variables, the matrix will have the form: 

            in_1  in_2 ...  in_N
   rule_1 [[mu_11 mu_12 ... mu_1N]
   rule_2  [mu_21 mu_22 ... mu_2N]
           [            ...      ]
   rule_Q  [mu_Q1 mu_Q2 ... mu_QN]]

Evaluation of hedges and "not": Each element of each FIS rule antecedent and consequent indicates the corresponding membership function, hedge, and whether or not "not" should be applied to the result. The index of the membership function to be used is given by the positive whole number portion of the antecedent/consequent vector entry, the hedge is given by the fractional portion (if any), and "not" is indicated by a minus sign. A "0" as the integer portion in any position in the rule indicates that the corresponding FIS input or output variable is omitted from the rule.

For custom hedges and the four built-in hedges "somewhat," "very," "extremely," and "very very," the membership function value (without the hedge or "not") is raised to the power corresponding to the hedge. All hedges are rounded to 2 digits.

For example, if "mu(x)" denotes the matching degree of the input to the corresponding membership function without a hedge or "not," then the final matching degree recorded in rule_input will be computed by applying the hedge and "not" in two steps. First, the hedge is applied: 

   (fraction == .05) <=>  somewhat x       <=>  mu(x)^0.5  <=>  sqrt(mu(x))
   (fraction == .20) <=>  very x           <=>  mu(x)^2    <=>  sqr(mu(x))
   (fraction == .30) <=>  extremely x      <=>  mu(x)^3    <=>  cube(mu(x))
   (fraction == .40) <=>  very very x      <=>  mu(x)^4
   (fraction == .dd) <=>  <custom hedge> x <=>  mu(x)^(dd/10)

After applying the appropriate hedge, "not" is calculated by: 

   minus sign present           <=> not x         <=> 1 - mu(x)
   minus sign and hedge present <=> not <hedge> x <=> 1 - mu(x)^(dd/10)

Hedges and "not" in the consequent are handled similarly.

The intermediate result rule_output: For either a Mamdani-type FIS (that is, an FIS that does not have constant or linear output membership functions) or a Sugeno-type FIS (that is, an FIS that has only constant and linear output membership functions), rule_output specifies the fuzzy output for each (rule, FIS output) pair. The format of rule_output depends on the FIS type.

For a Mamdani-type FIS, rule_output is a num_points x (Q * M) matrix, where Q is the number of rules and M is the number of FIS output variables. Each column of this matrix gives the y-values of the fuzzy output for a single (rule, FIS output) pair. 

                     Q cols            Q cols              Q cols 
                ---------------   ---------------     ---------------
                out_1 ... out_1   out_2 ... out_2 ... out_M ... out_M
            1 [[                                                     ]
            2  [                                                     ]
           ... [                                                     ]
   num_points  [                                                     ]]

For a Sugeno-type FIS, rule_output is a 2 x (Q * M) matrix. Each column of this matrix gives the (location, height) pair of the singleton output for a single (rule, FIS output) pair. 

                   Q cols            Q cols                  Q cols 
              ---------------   ---------------         ---------------
              out_1 ... out_1   out_2 ... out_2   ...   out_M ... out_M
   location [[                                                         ]
     height  [                                                         ]]

The intermediate result fuzzy_output: The format of fuzzy_output depends on the FIS type (’mamdani’ or ’sugeno’).

For either a Mamdani-type FIS or a Sugeno-type FIS, fuzzy_output specifies the aggregated fuzzy output for each FIS output.

For a Mamdani-type FIS, the aggregated fuzzy_output is a num_points x M matrix. Each column of this matrix gives the y-values of the fuzzy output for a single FIS output, aggregated over all rules. 

                out_1  out_2  ...  out_M
            1 [[                        ]
            2  [                        ]
           ... [                        ]
   num_points  [                        ]]

For a Sugeno-type FIS, the aggregated output for each FIS output is a 2 x L matrix, where L is the number of distinct singleton locations in the rule_output for that FIS output: 

              singleton_1  singleton_2 ... singleton_L
   location [[                                        ]
     height  [                                        ]]

Then fuzzy_output is a vector of M structures, each of which has an index and one of these matrices.

Examples: Five examples of using evalfis are shown in:

  • heart_disease_demo_2.m
  • investment_portfolio_demo.m
  • linear_tip_demo.m
  • mamdani_tip_demo.m
  • sugeno_tip_demo.m

See also: cubic_approx_demo, heart_disease_demo_1, heart_disease_demo_2, investment_portfolio_demo, linear_tip_demo, mamdani_tip_demo, sugeno_tip_demo

fuzzy-logic-toolkit-0.6.1/docs/evalmf.html000066400000000000000000000160011466512601400205560ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: evalmf

Function Reference: evalmf

Function File: y = evalmf (x, param, mf_type)
Function File: y = evalmf (x, param, mf_type, hedge)
Function File: y = evalmf (x, param, mf_type, hedge, not_flag)
Function File: y = evalmf ([x1 x2 ... xn], [param1 ... ], mf_type)
Function File: y = evalmf ([x1 x2 ... xn], [param1 ... ], mf_type, hedge)
Function File: y = evalmf ([x1 x2 ... xn], [param1 ... ], mf_type, hedge, not_flag)

For a given domain, set of parameters, membership function type, and optional hedge and not_flag, return the corresponding y-values for the membership function.

The argument x must be a real number or a non-empty list of strictly increasing real numbers, param must be a valid parameter or a vector of valid parameters for mf_type, and mf_type must be a string corresponding to a membership function type. Evalmf handles both built-in and custom membership functions.

For custom hedges and the four built-in hedges "somewhat", "very", "extremely", and "very very", raise the membership function values to the power corresponding to the hedge. 

   (fraction == .05) <=>  somewhat x       <=>  mu(x)^0.5  <=>  sqrt(mu(x))
   (fraction == .20) <=>  very x           <=>  mu(x)^2    <=>  sqr(mu(x))
   (fraction == .30) <=>  extremely x      <=>  mu(x)^3    <=>  cube(mu(x))
   (fraction == .40) <=>  very very x      <=>  mu(x)^4
   (fraction == .dd) <=>  <custom hedge> x <=>  mu(x)^(dd/10)

The not_flag negates the membership function using: 

   mu(not(x)) = 1 - mu(x)

To run the demonstration code, type "demo evalmf" (without the quotation marks) at the Octave prompt.

Example: 1

  

 x = 0:100;
 params = [25 50 75];
 mf_type = 'trimf';
 y = evalmf(x, params, mf_type);
 figure('NumberTitle', 'off', 'Name', "evalmf(0:100, [25 50 75], 'trimf')");
 plot(x, y, 'LineWidth', 2)
 ylim([-0.1 1.1]);
 xlabel('Crisp Input Value', 'FontWeight', 'bold');
 ylabel('Degree of Membership', 'FontWeight', 'bold');
 grid;
plotted figure

fuzzy-logic-toolkit-0.6.1/docs/fcm.html000066400000000000000000000426421466512601400200630ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: fcm

Function Reference: fcm

Function File: cluster_centers = fcm (input_data, num_clusters)
Function File: cluster_centers = fcm (input_data, num_clusters, options)
Function File: cluster_centers = fcm (input_data, num_clusters, [m, max_iterations, epsilon, display_intermediate_results])
Function File: [cluster_centers, soft_partition, obj_fcn_history] = fcm (input_data, num_clusters)
Function File: [cluster_centers, soft_partition, obj_fcn_history] = fcm (input_data, num_clusters, options)
Function File: [cluster_centers, soft_partition, obj_fcn_history] = fcm (input_data, num_clusters, [m, max_iterations, epsilon, display_intermediate_results])

Using the Fuzzy C-Means algorithm, calculate and return the soft partition of a set of unlabeled data points.

Also, if display_intermediate_results is true, display intermediate results after each iteration. Note that because the initial cluster prototypes are randomly selected locations in the ranges determined by the input data, the results of this function are nondeterministic.

The required arguments to fcm are:

  • input_data: a matrix of input data points; each row corresponds to one point
  • num_clusters: the number of clusters to form

The optional arguments to fcm are:

  • m: the parameter (exponent) in the objective function; default = 2.0
  • max_iterations: the maximum number of iterations before stopping; default = 100
  • epsilon: the stopping criteria; default = 1e-5
  • display_intermediate_results: if 1, display results after each iteration, and if 0, do not; default = 1

The default values are used if any of the optional arguments are missing or evaluate to NaN.

The return values are:

  • cluster_centers: a matrix of the cluster centers; each row corresponds to one point
  • soft_partition: a constrained soft partition matrix
  • obj_fcn_history: the values of the objective function after each iteration

Three important matrices used in the calculation are X (the input points to be clustered), V (the cluster centers), and Mu (the membership of each data point in each cluster). Each row of X and V denotes a single point, and Mu(i, j) denotes the membership degree of input point X(j, :) in the cluster having center V(i, :).

X is identical to the required argument input_data; V is identical to the output cluster_centers; and Mu is identical to the output soft_partition.

If n denotes the number of input points and k denotes the number of clusters to be formed, then X, V, and Mu have the dimensions: 

                                     1    2   ...  #features
                               1 [[                           ]
    X  =  input_data       =   2  [                           ]
                              ... [                           ]
                               n  [                           ]]

                                     1    2   ...  #features
                               1 [[                           ]
    V  =  cluster_centers  =   2  [                           ]
                              ... [                           ]
                               k  [                           ]]

                                     1    2   ...   n
                               1 [[                    ]
    Mu  =  soft_partition  =   2  [                    ]
                              ... [                    ]
                               k  [                    ]]

See also: gustafson_kessel, partition_coeff, partition_entropy, xie_beni_index

Example: 1

  

 ## This demo:
 ##    - classifies a small set of unlabeled data points using
 ##      the Fuzzy C-Means algorithm into two fuzzy clusters
 ##    - plots the input points together with the cluster centers
 ##    - evaluates the quality of the resulting clusters using
 ##      three validity measures: the partition coefficient, the
 ##      partition entropy, and the Xie-Beni validity index
 ##
 ## Note: The input_data is taken from Chapter 13, Example 17 in
 ##       Fuzzy Logic: Intelligence, Control and Information, by
 ##       J. Yen and R. Langari, Prentice Hall, 1999, page 381
 ##       (International Edition). 

 ## Use fcm to classify the input_data.
 input_data = [2 12; 4 9; 7 13; 11 5; 12 7; 14 4];
 number_of_clusters = 2;
 [cluster_centers, soft_partition, obj_fcn_history] = ...
   fcm (input_data, number_of_clusters)
 
 ## Plot the data points as small blue x's.
 figure ('NumberTitle', 'off', 'Name', 'FCM Demo 1');
 for i = 1 : rows (input_data)
   plot (input_data(i, 1), input_data(i, 2), 'LineWidth', 2, ...
         'marker', 'x', 'color', 'b');
   hold on;
 endfor

 ## Plot the cluster centers as larger red *'s.
 for i = 1 : number_of_clusters
   plot (cluster_centers(i, 1), cluster_centers(i, 2), ...
         'LineWidth', 4, 'marker', '*', 'color', 'r');
   hold on;
 endfor

 ## Make the figure look a little better:
 ##    - scale and label the axes
 ##    - show gridlines
 xlim ([0 15]);
 ylim ([0 15]);
 xlabel ('Feature 1');
 ylabel ('Feature 2');
 grid
 hold
 
 ## Calculate and print the three validity measures.
 printf ("Partition Coefficient: %f\n", ...
         partition_coeff (soft_partition));
 printf ("Partition Entropy (with a = 2): %f\n", ...
         partition_entropy (soft_partition, 2));
 printf ("Xie-Beni Index: %f\n\n", ...
         xie_beni_index (input_data, cluster_centers, ...
         soft_partition));

Iteration count = 1,  Objective fcn = 48.836786
Iteration count = 2,  Objective fcn = 28.958626
Iteration count = 3,  Objective fcn = 28.758695
Iteration count = 4,  Objective fcn = 28.757469
Iteration count = 5,  Objective fcn = 28.757461
Iteration count = 6,  Objective fcn = 28.757460
Iteration count = 7,  Objective fcn = 28.757460
Iteration count = 8,  Objective fcn = 28.757460
cluster_centers =

    4.2023   11.2805
   12.2859    5.3691

soft_partition =

   0.965400   0.939806   0.888774   0.020467   0.033486   0.031290
   0.034600   0.060194   0.111226   0.979533   0.966514   0.968710

obj_fcn_history =

   48.837   28.959   28.759   28.757   28.757   28.757   28.757   28.757

hold is now off for current axes
Partition Coefficient: 0.909483
Partition Entropy (with a = 2): 0.267539
Xie-Beni Index: 0.095582
plotted figure

Example: 2

  

 ## This demo:
 ##    - classifies three-dimensional unlabeled data points using
 ##      the Fuzzy C-Means algorithm into three fuzzy clusters
 ##    - plots the input points together with the cluster centers
 ##    - evaluates the quality of the resulting clusters using
 ##      three validity measures: the partition coefficient, the
 ##      partition entropy, and the Xie-Beni validity index
 ##
 ## Note: The input_data was selected to form three areas of
 ##       different shapes.
 
 ## Use fcm to classify the input_data.
 input_data = [1 11 5; 1 12 6; 1 13 5; 2 11 7; 2 12 6; 2 13 7;
               3 11 6; 3 12 5; 3 13 7; 1 1 10; 1 3 9; 2 2 11;
               3 1 9; 3 3 10; 3 5 11; 4 4 9; 4 6 8; 5 5 8; 5 7 9;
               6 6 10; 9 10 12; 9 12 13; 9 13 14; 10 9 13; 10 13 12;
               11 10 14; 11 12 13; 12 6 12; 12 7 15; 12 9 15;
               14 6 14; 14 8 13];
 number_of_clusters = 3;
 [cluster_centers, soft_partition, obj_fcn_history] = ...
   fcm (input_data, number_of_clusters, [NaN NaN NaN 0])
 
 ## Plot the data points in two dimensions (using features 1 & 2)
 ## as small blue x's.
 figure ('NumberTitle', 'off', 'Name', 'FCM Demo 2');
 for i = 1 : rows (input_data)
   plot (input_data(i, 1), input_data(i, 2), 'LineWidth', 2, ...
         'marker', 'x', 'color', 'b');
   hold on;
 endfor
 
 ## Plot the cluster centers in two dimensions
 ## (using features 1 & 2) as larger red *'s.
 for i = 1 : number_of_clusters
   plot (cluster_centers(i, 1), cluster_centers(i, 2), ...
         'LineWidth', 4, 'marker', '*', 'color', 'r');
   hold on;
 endfor
 
 ## Make the figure look a little better:
 ##    - scale and label the axes
 ##    - show gridlines
 xlim ([0 15]);
 ylim ([0 15]);
 xlabel ('Feature 1');
 ylabel ('Feature 2');
 grid
 hold
 
 ## Plot the data points in two dimensions
 ## (using features 1 & 3) as small blue x's.
 figure ('NumberTitle', 'off', 'Name', 'FCM Demo 2');
 for i = 1 : rows (input_data)
   plot (input_data(i, 1), input_data(i, 3), 'LineWidth', 2, ...
         'marker', 'x', 'color', 'b');
   hold on;
 endfor
 
 ## Plot the cluster centers in two dimensions
 ## (using features 1 & 3) as larger red *'s.
 for i = 1 : number_of_clusters
   plot (cluster_centers(i, 1), cluster_centers(i, 3), ...
         'LineWidth', 4, 'marker', '*', 'color', 'r');
   hold on;
 endfor
 
 ## Make the figure look a little better:
 ##    - scale and label the axes
 ##    - show gridlines
 xlim ([0 15]);
 ylim ([0 15]);
 xlabel ('Feature 1');
 ylabel ('Feature 3');
 grid
 hold
 
 ## Calculate and print the three validity measures.
 printf ("Partition Coefficient: %f\n", ...
         partition_coeff (soft_partition));
 printf ("Partition Entropy (with a = 2): %f\n", ...
         partition_entropy (soft_partition, 2));
 printf ("Xie-Beni Index: %f\n\n", ...
         xie_beni_index (input_data, cluster_centers, ...
         soft_partition));

cluster_centers =

    3.1989    3.6232    9.5521
    2.0937   11.9016    6.0942
   11.0424    9.5332   13.3569

soft_partition =

 Columns 1 through 6:

   3.7871e-02   1.3572e-02   3.0172e-02   2.5327e-02   3.2448e-04   2.0488e-02
   9.4461e-01   9.7904e-01   9.5109e-01   9.6197e-01   9.9948e-01   9.6487e-01
   1.7523e-02   7.3841e-03   1.8740e-02   1.2705e-02   1.9250e-04   1.4638e-02

 Columns 7 through 12:

   2.3598e-02   2.1516e-02   2.8591e-02   8.6766e-01   9.1223e-01   9.1464e-01
   9.6332e-01   9.6457e-01   9.4834e-01   7.6424e-02   5.6743e-02   4.6202e-02
   1.3086e-02   1.3915e-02   2.3066e-02   5.5911e-02   3.1032e-02   3.9162e-02

 Columns 13 through 18:

   9.0697e-01   9.8825e-01   9.0909e-01   9.7506e-01   7.6774e-01   8.2343e-01
   5.1152e-02   6.5170e-03   5.0542e-02   1.4244e-02   1.5868e-01   1.0410e-01
   4.1879e-02   5.2361e-03   4.0373e-02   1.0700e-02   7.3582e-02   7.2479e-02

 Columns 19 through 24:

   6.2230e-01   6.7200e-01   6.7469e-02   7.4870e-02   9.2741e-02   1.6712e-02
   2.2741e-01   1.4085e-01   6.2864e-02   9.0815e-02   1.1768e-01   1.2265e-02
   1.5029e-01   1.8715e-01   8.6967e-01   8.3432e-01   7.8958e-01   9.7102e-01

 Columns 25 through 30:

   8.4745e-02   5.1715e-03   3.9804e-02   1.3556e-01   7.4614e-02   2.7318e-02
   1.2048e-01   4.3134e-03   4.4784e-02   7.1964e-02   4.3901e-02   1.9996e-02
   7.9477e-01   9.9052e-01   9.1541e-01   7.9248e-01   8.8149e-01   9.5269e-01

 Columns 31 and 32:

   1.2256e-01   6.7204e-02
   7.2840e-02   4.8500e-02
   8.0460e-01   8.8430e-01

obj_fcn_history =

 Columns 1 through 10:

   408.08   240.46   184.85   181.00   180.66   180.61   180.61   180.61   180.61   180.61

 Columns 11 through 16:

   180.61   180.61   180.61   180.61   180.61   180.61

hold is now off for current axes
hold is now off for current axes
Partition Coefficient: 0.813224
Partition Entropy (with a = 2): 0.541401
Xie-Beni Index: 0.207218
plotted figure

plotted figure

fuzzy-logic-toolkit-0.6.1/docs/gauss2mf.html000066400000000000000000000162221466512601400210400ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: gauss2mf

Function Reference: gauss2mf

Function File: y = gauss2mf (x, params)
Function File: y = gauss2mf ([x1 x2 ... xn], [sig1 c1 sig2 c2])

For a given domain x and parameters params (or [sig1 c1 sig2 c2]), return the corresponding y values for the two-sided Gaussian composite membership function. This membership function is a smooth curve calculated from two Gaussian membership functions as follows:

Given parameters sig1, c1, sig2, and c2, that define two Gaussian membership functions, let: 

     f1(x) = exp((-(x - c1)^2)/(2 * sig1^2))    if x <= c1
             1                                  otherwise

     f2(x) = 1                                  if x <= c2
             exp((-(x - c2)^2)/(2 * sig2^2))    otherwise

Then gauss2mf is given by: 

     f(x) = f1(x) * f2(x)

The argument x must be a real number or a non-empty vector of strictly increasing real numbers, and sig1, c1, sig2, and c2 must be real numbers. Gauss2mf always returns a continuously differentiable curve with values in the range [0, 1].

If c1 < c2, gauss2mf is a normal membership function (has a maximum value of 1), with the rising curve identical to that of f1(x) and a falling curve identical to that of f2(x), above. If c1 >= c2, gauss2mf returns a subnormal membership function (has a maximum value less than 1).

To run the demonstration code, type "demo gauss2mf" (without the quotation marks) at the Octave prompt.

See also: dsigmf, gaussmf, gbellmf, pimf, psigmf, sigmf, smf, trapmf, trimf, zmf

Example: 1

  

 x = -10:0.2:10;
 params = [3 0 1.5 2];
 y1 = gauss2mf(x, params);
 params = [1.5 0 3 2];
 y2 = gauss2mf(x, params);
 params = [1.5 2 3 0];
 y3 = gauss2mf(x, params);
 figure('NumberTitle', 'off', 'Name', 'gauss2mf demo');
 plot(x, y1, 'r;params = [3 0 1.5 2];', 'LineWidth', 2);
 hold on ;
 plot(x, y2, 'b;params = [1.5 0 3 2];', 'LineWidth', 2);
 hold on ;
 plot(x, y3, 'g;params = [1.5 2 3 0];', 'LineWidth', 2);
 ylim([-0.1 1.1]);
 xlabel('Crisp Input Value', 'FontWeight', 'bold');
 ylabel('Degree of Membership', 'FontWeight', 'bold');
 grid;
 hold;

hold is now off for current axes
plotted figure

fuzzy-logic-toolkit-0.6.1/docs/gaussmf.html000066400000000000000000000154471466512601400207660ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: gaussmf

Function Reference: gaussmf

Function File: y = gaussmf (x, params)
Function File: y = gaussmf ([x1 x2 ... xn], [sig c])

For a given domain x and parameters params (or [sig c]), return the corresponding y values for the Gaussian membership function. This membership function is shaped like the Gaussian (normal) distribution, but scaled to have a maximum value of 1. By contrast, the area under the Gaussian distribution curve is 1.

The argument x must be a real number or a non-empty vector of strictly increasing real numbers, and sig and c must be real numbers. This membership function satisfies the equation: 

     f(x) = exp((-(x - c)^2)/(2 * sig^2))

which always returns values in the range [0, 1].

Just as for the Gaussian (normal) distribution, the parameters sig and c represent: 

     sig^2 == the variance (a measure of the width of the curve)
         c == the center (the mean; the x value of the peak)

For larger values of sig, the curve is flatter, and for smaller values of sig, the curve is narrower. The y value at the center is always 1: 

     f(c) == 1

To run the demonstration code, type "demo gaussmf" (without the quotation marks) at the Octave prompt.

See also: dsigmf, gauss2mf, gbellmf, pimf, psigmf, sigmf, smf, trapmf, trimf, zmf

Example: 1

  

 x = -5:0.1:5;
 params = [0.5 0];
 y1 = gaussmf(x, params);
 params = [1 0];
 y2 = gaussmf(x, params);
 params = [2 0];
 y3 = gaussmf(x, params);
 figure('NumberTitle', 'off', 'Name', 'gaussmf demo');
 plot(x, y1, 'r;params = [0.5 0];', 'LineWidth', 2);
 hold on ;
 plot(x, y2, 'b;params = [1 0];', 'LineWidth', 2);
 hold on ;
 plot(x, y3, 'g;params = [2 0];', 'LineWidth', 2);
 ylim([-0.1 1.1]);
 xlabel('Crisp Input Value');
 ylabel('Degree of Membership');
 grid;
 hold;

hold is now off for current axes
plotted figure

fuzzy-logic-toolkit-0.6.1/docs/gbellmf.html000066400000000000000000000157201466512601400207230ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: gbellmf

Function Reference: gbellmf

Function File: y = gbellmf (x, params)
Function File: y = gbellmf ([x1 x2 ... xn], [a b c])

For a given domain x and parameters params (or [a b c]), return the corresponding y values for the generalized bell-shaped membership function.

The argument x must be a real number or a non-empty vector of strictly increasing real numbers, a, b, and c must be real numbers, a must be non-zero, and b must be an integer. This membership function satisfies the equation: 

     f(x) = 1/(1 + (abs((x - c)/a))^(2 * b))

which always returns values in the range [0, 1].

The parameters a, b, and c give: 

     a == controls the width of the curve at f(x) = 0.5;
          f(c-a) = f(c+a) = 0.5
     b == controls the slope of the curve at x = c-a and x = c+a;
          f'(c-a) = b/2a and f'(c+a) = -b/2a
     c == the center of the curve

This membership function has a value of 0.5 at the two points c - a and c + a, and the width of the curve at f(x) == 0.5 is 2 * |a|: 

     f(c - a) == f(c + a) == 0.5
     2 * |a| == the width of the curve at f(x) == 0.5

The generalized bell-shaped membership function is continuously differentiable and is symmetric about the line x = c.

To run the demonstration code, type "demo gbellmf" (without the quotation marks) at the Octave prompt.

See also: dsigmf, gauss2mf, gaussmf, pimf, psigmf, sigmf, smf, trapmf, trimf, zmf

Example: 1

  

 x = 0:255;
 params = [20 4 100];
 y1 = gbellmf(x, params);
 params = [30 3 100];
 y2 = gbellmf(x, params);
 params = [40 2 100];
 y3 = gbellmf(x, params);
 figure('NumberTitle', 'off', 'Name', 'gbellmf demo');
 plot(x, y1, 'r;params = [20 4 100];', 'LineWidth', 2)
 hold on;
 plot(x, y2, 'b;params = [30 3 100];', 'LineWidth', 2)
 hold on;
 plot(x, y3, 'g;params = [40 2 100];', 'LineWidth', 2)
 ylim([-0.1 1.1]);
 xlabel('Crisp Input Value', 'FontWeight', 'bold');
 ylabel('Degree of Membership', 'FontWeight', 'bold');
 grid;
plotted figure

fuzzy-logic-toolkit-0.6.1/docs/gensurf.html000066400000000000000000000136711466512601400207670ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: gensurf

Function Reference: gensurf

Function File: gensurf (fis)
Function File: gensurf (fis, input_axes)
Function File: gensurf (fis, input_axes, output_axes)
Function File: gensurf (fis, input_axes, output_axes, grids)
Function File: gensurf (fis, input_axes, output_axes, grids, ref_input)
Function File: gensurf (fis, input_axes, output_axes, grids, ref_input, num_points)
Function File: [x, y, z] = gensurf (...)

Generate and plot a surface (or 2-dimensional curve) showing one FIS output as a function of two (or one) of the FIS inputs. The reference input is used for all FIS inputs that are not in the input_axes vector.

Grids, which specifies the number of grids to show on the input axes, may be a scalar or a vector of length 2. If a scalar, then both axes will use the same number of grids. If a vector of length 2, then the grids on the two axes are controlled separately.

Num_points specifies the number of points to use when evaluating the FIS.

The final form "[x, y, z] = gensurf(...)" suppresses plotting.

Default values for arguments not supplied are:

  • input_axes == [1 2]
  • output_axis == 1
  • grids == [15 15]
  • ref_input == []
  • num_points == 101

Six demo scripts that use gensurf are:

  • cubic_approx_demo.m
  • heart_disease_demo_1.m
  • heart_disease_demo_2.m
  • investment_portfolio_demo.m
  • linear_tip_demo.m
  • mamdani_tip_demo.m
  • sugeno_tip_demo.m

Current limitation: The form of gensurf that suppresses plotting (the final form above) is not yet implemented.

See also: cubic_approx_demo, heart_disease_demo_1, heart_disease_demo_2, investment_portfolio_demo, linear_tip_demo, mamdani_tip_demo, sugeno_tip_demo, plotmf

fuzzy-logic-toolkit-0.6.1/docs/getfis.html000066400000000000000000000175331466512601400206000ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: getfis

Function Reference: getfis

Function File: retval = getfis (fis)
Function File: retval = getfis (fis, property)
Function File: retval = getfis (fis, in_or_out, var_index)
Function File: retval = getfis (fis, in_or_out, var_index, var_property)
Function File: retval = getfis (fis, in_or_out, var_index, mf, mf_index)
Function File: retval = getfis (fis, in_or_out, var_index, mf, mf_index, mf_property)

Return or print the property (field) values of an FIS structure specified by the arguments.

There are six forms of getfis:

Number of ArgumentsAction Taken
1Print (some) properties of an FIS structure on standard output. Return the empty set.
2Return a specified property of the FIS structure. The properties that may be specified are: name, type, version, numinputs, numoutputs, numinputmfs, numoutputmfs, numrules, andmethod, ormethod, impmethod, addmethod, defuzzmethod, inlabels, outlabels, inrange, outrange, inmfs, outmfs, inmflabels, outmflabels, inmftypes, outmftypes, inmfparams, outmfparams, and rulelist.
3Print the properties of a specified input or output variable of the FIS structure. Return the empty set.
4Return a specified property of an input or output variable. The properties that may be specified are: name, range, nummfs, and mflabels.
5Print the properties of a specified membership function of the FIS structure. Return the empty set.
6Return a specified property of a membership function. The properties that may be specified are: name, type, and params.

The types/values of the arguments are expected to be:

ArgumentExpected Type or Value
fisan FIS structure
propertya string; one of: ’name’, ’type’, ’version’, ’numinputs’, ’numoutputs’, ’numinputmfs’, ’numoutputmfs’, ’numrules’, ’andmethod’, ’ormethod’, ’impmethod’, ’addmethod’, ’defuzzmethod’ ’inlabels’, ’outlabels’, ’inrange’, ’outrange’, ’inmfs’, ’outmfs’, ’inmflabels’, ’outmflabels’, ’inmftypes’, ’outmftypes’, ’inmfparams’, ’outmfparams’, and ’rulelist’ (case-insensitive)
in_or_outeither ’input’ or ’output’ (case-insensitive)
var_indexa valid integer index of an input or output FIS variable
var_propertya string; one of: ’name’, ’range’, ’nummfs’, and ’mflabels’
mfthe string ’mf’
mf_indexa valid integer index of a membership function
mf_propertya string; one of ’name’, ’type’, or ’params’

Note that all of the strings representing properties above are case insensitive.

See also: setfis, showfis

fuzzy-logic-toolkit-0.6.1/docs/gustafson_kessel.html000066400000000000000000000470111466512601400226700ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: gustafson_kessel

Function Reference: gustafson_kessel

Function File: cluster_centers = gustafson_kessel (input_data, num_clusters)
Function File: cluster_centers = gustafson_kessel (input_data, num_clusters, cluster_volume)
Function File: cluster_centers = gustafson_kessel (input_data, num_clusters, cluster_volume, options)
Function File: cluster_centers = gustafson_kessel (input_data, num_clusters, cluster_volume, [m, max_iterations, epsilon, display_intermediate_results])
Function File: [cluster_centers, soft_partition, obj_fcn_history] = gustafson_kessel (input_data, num_clusters)
Function File: [cluster_centers, soft_partition, obj_fcn_history] = gustafson_kessel (input_data, num_clusters, cluster_volume)
Function File: [cluster_centers, soft_partition, obj_fcn_history] = gustafson_kessel (input_data, num_clusters, cluster_volume, options)
Function File: [cluster_centers, soft_partition, obj_fcn_history] = gustafson_kessel (input_data, num_clusters, cluster_volume, [m, max_iterations, epsilon, display_intermediate_results])

Using the Gustafson-Kessel algorithm, calculate and return the soft partition of a set of unlabeled data points.

Also, if display_intermediate_results is true, display intermediate results after each iteration. Note that because the initial cluster prototypes are randomly selected locations in the ranges determined by the input data, the results of this function are nondeterministic.

The required arguments to gustafson_kessel are:

  • input_data: a matrix of input data points; each row corresponds to one point
  • num_clusters: the number of clusters to form

The third (optional) argument to gustafson_kessel is a vector of cluster volumes. If omitted, a vector of 1’s will be used as the default.

The fourth (optional) argument to gustafson_kessel is a vector consisting of:

  • m: the parameter (exponent) in the objective function; default = 2.0
  • max_iterations: the maximum number of iterations before stopping; default = 100
  • epsilon: the stopping criteria; default = 1e-5
  • display_intermediate_results: if 1, display results after each iteration, and if 0, do not; default = 1

The default values are used if any of the four elements of the vector are missing or evaluate to NaN.

The return values are:

  • cluster_centers: a matrix of the cluster centers; each row corresponds to one point
  • soft_partition: a constrained soft partition matrix
  • obj_fcn_history: the values of the objective function after each iteration

Three important matrices used in the calculation are X (the input points to be clustered), V (the cluster centers), and Mu (the membership of each data point in each cluster). Each row of X and V denotes a single point, and Mu(i, j) denotes the membership degree of input point X(j, :) in the cluster having center V(i, :).

X is identical to the required argument input_data; V is identical to the output cluster_centers; and Mu is identical to the output soft_partition.

If n denotes the number of input points and k denotes the number of clusters to be formed, then X, V, and Mu have the dimensions: 

                                     1    2   ...  #features
                               1 [[                           ]
    X  =  input_data       =   2  [                           ]
                              ... [                           ]
                               n  [                           ]]

                                     1    2   ...  #features
                               1 [[                           ]
    V  =  cluster_centers  =   2  [                           ]
                              ... [                           ]
                               k  [                           ]]

                                     1    2   ...   n
                               1 [[                    ]
    Mu  =  soft_partition  =   2  [                    ]
                              ... [                    ]
                               k  [                    ]]

See also: fcm, partition_coeff, partition_entropy, xie_beni_index

Example: 1

  

 ## This demo:
 ##    - classifies a small set of unlabeled data points using
 ##      the Gustafson-Kessel algorithm into two fuzzy clusters
 ##    - plots the input points together with the cluster centers
 ##    - evaluates the quality of the resulting clusters using
 ##      three validity measures: the partition coefficient, the
 ##      partition entropy, and the Xie-Beni validity index
 ##
 ## Note: The input_data is taken from Chapter 13, Example 17 in
 ##       Fuzzy Logic: Intelligence, Control and Information, by
 ##       J. Yen and R. Langari, Prentice Hall, 1999, page 381
 ##       (International Edition). 
 
 ## Use gustafson_kessel to classify the input_data.
 input_data = [2 12; 4 9; 7 13; 11 5; 12 7; 14 4];
 number_of_clusters = 2;
 [cluster_centers, soft_partition, obj_fcn_history] = ...
   gustafson_kessel (input_data, number_of_clusters)
 
 ## Plot the data points as small blue x's.
 figure ('NumberTitle', 'off', 'Name', 'Gustafson-Kessel Demo 1');
 for i = 1 : rows (input_data)
   plot (input_data(i, 1), input_data(i, 2), 'LineWidth', 2, ...
         'marker', 'x', 'color', 'b');
   hold on;
 endfor
 
 ## Plot the cluster centers as larger red *'s.
 for i = 1 : number_of_clusters
   plot (cluster_centers(i, 1), cluster_centers(i, 2), ...
         'LineWidth', 4, 'marker', '*', 'color', 'r');
   hold on;
 endfor
 
 ## Make the figure look a little better:
 ##    - scale and label the axes
 ##    - show gridlines
 xlim ([0 15]);
 ylim ([0 15]);
 xlabel ('Feature 1');
 ylabel ('Feature 2');
 grid
 hold
 
 ## Calculate and print the three validity measures.
 printf ("Partition Coefficient: %f\n", ...
         partition_coeff (soft_partition));
 printf ("Partition Entropy (with a = 2): %f\n", ...
         partition_entropy (soft_partition, 2));
 printf ("Xie-Beni Index: %f\n\n", ...
         xie_beni_index (input_data, cluster_centers, ...
         soft_partition));

Iteration count = 1,  Objective fcn = 32.036570
Iteration count = 2,  Objective fcn = 26.486425
Iteration count = 3,  Objective fcn = 26.199786
Iteration count = 4,  Objective fcn = 25.994545
Iteration count = 5,  Objective fcn = 25.831740
Iteration count = 6,  Objective fcn = 25.730027
Iteration count = 7,  Objective fcn = 25.679108
Iteration count = 8,  Objective fcn = 25.657508
Iteration count = 9,  Objective fcn = 25.649243
Iteration count = 10,  Objective fcn = 25.646251
Iteration count = 11,  Objective fcn = 25.645199
Iteration count = 12,  Objective fcn = 25.644835
Iteration count = 13,  Objective fcn = 25.644709
Iteration count = 14,  Objective fcn = 25.644666
Iteration count = 15,  Objective fcn = 25.644652
Iteration count = 16,  Objective fcn = 25.644647
Iteration count = 17,  Objective fcn = 25.644645
Iteration count = 18,  Objective fcn = 25.644644
Iteration count = 19,  Objective fcn = 25.644644
Iteration count = 20,  Objective fcn = 25.644644
Iteration count = 21,  Objective fcn = 25.644644
Iteration count = 22,  Objective fcn = 25.644644
Iteration count = 23,  Objective fcn = 25.644644
Iteration count = 24,  Objective fcn = 25.644644
Iteration count = 25,  Objective fcn = 25.644644
cluster_centers =

    4.2228   11.3276
   12.2661    5.3877

soft_partition =

   0.934026   0.890527   0.870501   0.023530   0.028088   0.012592
   0.065974   0.109473   0.129499   0.976470   0.971912   0.987408

obj_fcn_history =

 Columns 1 through 10:

   32.037   26.486   26.200   25.995   25.832   25.730   25.679   25.658   25.649   25.646

 Columns 11 through 20:

   25.645   25.645   25.645   25.645   25.645   25.645   25.645   25.645   25.645   25.645

 Columns 21 through 25:

   25.645   25.645   25.645   25.645   25.645

hold is now off for current axes
Partition Coefficient: 0.888484
Partition Entropy (with a = 2): 0.308027
Xie-Beni Index: 0.107028
plotted figure

Example: 2

  

 ## This demo:
 ##    - classifies three-dimensional unlabeled data points using
 ##      the Gustafson-Kessel algorithm into three fuzzy clusters
 ##    - plots the input points together with the cluster centers
 ##    - evaluates the quality of the resulting clusters using
 ##      three validity measures: the partition coefficient, the
 ##      partition entropy, and the Xie-Beni validity index
 ##
 ## Note: The input_data was selected to form three areas of
 ##       different shapes.
 
 ## Use gustafson_kessel to classify the input_data.
 input_data = [1 11 5; 1 12 6; 1 13 5; 2 11 7; 2 12 6; 2 13 7;
               3 11 6; 3 12 5; 3 13 7; 1 1 10; 1 3 9; 2 2 11;
               3 1 9; 3 3 10; 3 5 11; 4 4 9; 4 6 8; 5 5 8; 5 7 9;
               6 6 10; 9 10 12; 9 12 13; 9 13 14; 10 9 13; 10 13 12;
               11 10 14; 11 12 13; 12 6 12; 12 7 15; 12 9 15;
               14 6 14; 14 8 13];
 number_of_clusters = 3;
 [cluster_centers, soft_partition, obj_fcn_history] = ...
   gustafson_kessel (input_data, number_of_clusters, [1 1 1], ...
                     [NaN NaN NaN 0])
 
 ## Plot the data points in two dimensions (using features 1 & 2)
 ## as small blue x's.
 figure ('NumberTitle', 'off', 'Name', 'Gustafson-Kessel Demo 2');
 for i = 1 : rows (input_data)
   plot (input_data(i, 1), input_data(i, 2), 'LineWidth', 2, ...
         'marker', 'x', 'color', 'b');
   hold on;
 endfor
 
 ## Plot the cluster centers in two dimensions
 ## (using features 1 & 2) as larger red *'s.
 for i = 1 : number_of_clusters
   plot (cluster_centers(i, 1), cluster_centers(i, 2), ...
         'LineWidth', 4, 'marker', '*', 'color', 'r');
   hold on;
 endfor
 
 ## Make the figure look a little better:
 ##    - scale and label the axes
 ##    - show gridlines
 xlim ([0 15]);
 ylim ([0 15]);
 xlabel ('Feature 1');
 ylabel ('Feature 2');
 grid
  
 ## Plot the data points in two dimensions
 ## (using features 1 & 3) as small blue x's.
 figure ('NumberTitle', 'off', 'Name', 'Gustafson-Kessel Demo 2');
 for i = 1 : rows (input_data)
   plot (input_data(i, 1), input_data(i, 3), 'LineWidth', 2, ...
         'marker', 'x', 'color', 'b');
   hold on;
 endfor
 
 ## Plot the cluster centers in two dimensions
 ## (using features 1 & 3) as larger red *'s.
 for i = 1 : number_of_clusters
   plot (cluster_centers(i, 1), cluster_centers(i, 3), ...
         'LineWidth', 4, 'marker', '*', 'color', 'r');
   hold on;
 endfor
 
 ## Make the figure look a little better:
 ##    - scale and label the axes
 ##    - show gridlines
 xlim ([0 15]);
 ylim ([0 15]);
 xlabel ('Feature 1');
 ylabel ('Feature 3');
 grid
 hold
 
 ## Calculate and print the three validity measures.
 printf ("Partition Coefficient: %f\n", ...
         partition_coeff (soft_partition));
 printf ("Partition Entropy (with a = 2): %f\n", ...
         partition_entropy (soft_partition, 2));
 printf ("Xie-Beni Index: %f\n\n", ...
         xie_beni_index (input_data, cluster_centers, ...
         soft_partition));

cluster_centers =

   11.1675    9.5123   13.4360
    2.0744   11.9210    6.0810
    3.2679    3.7416    9.5189

soft_partition =

 Columns 1 through 6:

   1.1157e-02   7.1682e-03   9.2570e-03   1.3792e-02   6.1636e-05   1.8522e-02
   9.6971e-01   9.8313e-01   9.8010e-01   9.6123e-01   9.9985e-01   9.6174e-01
   1.9130e-02   9.7022e-03   1.0643e-02   2.4973e-02   8.9272e-05   1.9737e-02

 Columns 7 through 12:

   1.0694e-02   2.5264e-02   2.0999e-02   9.2634e-03   1.8979e-02   1.3117e-02
   9.6753e-01   9.3340e-01   9.5532e-01   2.2956e-02   6.1145e-02   2.9746e-02
   2.1778e-02   4.1336e-02   2.3681e-02   9.6778e-01   9.1988e-01   9.5714e-01

 Columns 13 through 18:

   2.2734e-02   2.4881e-03   3.1043e-02   4.4868e-03   2.9448e-02   2.6948e-02
   5.6777e-02   6.5225e-03   7.9769e-02   1.3945e-02   1.4999e-01   9.6884e-02
   9.2049e-01   9.9099e-01   8.8919e-01   9.8157e-01   8.2056e-01   8.7617e-01

 Columns 19 through 24:

   3.3446e-02   5.4461e-02   7.2961e-01   9.0208e-01   8.6338e-01   9.0000e-01
   1.4314e-01   1.2767e-01   1.3230e-01   5.3105e-02   7.6953e-02   5.2614e-02
   8.2342e-01   8.1786e-01   1.3809e-01   4.4813e-02   5.9663e-02   4.7385e-02

 Columns 25 through 30:

   7.8178e-01   9.8041e-01   8.8736e-01   8.1782e-01   8.9517e-01   9.2117e-01
   1.0864e-01   1.0972e-02   5.8405e-02   1.0065e-01   6.3515e-02   4.6914e-02
   1.0958e-01   8.6145e-03   5.4237e-02   8.1536e-02   4.1313e-02   3.1917e-02

 Columns 31 and 32:

   9.3144e-01   8.7447e-01
   4.2581e-02   7.2530e-02
   2.5982e-02   5.3000e-02

obj_fcn_history =

 Columns 1 through 10:

   231.36   183.01   167.78   158.16   149.79   141.02   133.08   127.09   123.40   121.53

 Columns 11 through 20:

   120.64   120.26   120.11   120.06   120.04   120.04   120.03   120.03   120.03   120.03

 Columns 21 through 30:

   120.03   120.03   120.03   120.03   120.03   120.03   120.03   120.03   120.03   120.03

hold is now off for current axes
Partition Coefficient: 0.841843
Partition Entropy (with a = 2): 0.472418
Xie-Beni Index: 0.192630
plotted figure

plotted figure

fuzzy-logic-toolkit-0.6.1/docs/hamacher_product.html000066400000000000000000000112541466512601400226210ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: hamacher_product

Function Reference: hamacher_product

Function File: retval = hamacher_product (x)
Function File: retval = hamacher_product (x, y)

Return the Hamacher product of the input. The Hamacher product of two real scalars x and y is: (x * y) / (x + y - x * y)

For one vector argument, apply the Hamacher product to all of the elements of the vector. (The Hamacher product is associative.) For one two-dimensional matrix argument, return a vector of the Hamacher product of each column.

For two vectors or matrices of identical dimensions, or for one scalar and one vector or matrix argument, return the pairwise Hamacher product.

See also: algebraic_product, algebraic_sum, bounded_difference, bounded_sum, drastic_product, drastic_sum, einstein_product, einstein_sum, hamacher_sum

fuzzy-logic-toolkit-0.6.1/docs/hamacher_sum.html000066400000000000000000000112241466512601400217420ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: hamacher_sum

Function Reference: hamacher_sum

Function File: retval = hamacher_sum (x)
Function File: retval = hamacher_sum (x, y)

Return the Hamacher sum of the input. The Hamacher sum of two real scalars x and y is: (x + y - 2 * x * y) / (1 - x * y)

For one vector argument, apply the Hamacher sum to all of the elements of the vector. (The Hamacher sum is associative.) For one two-dimensional matrix argument, return a vector of the Hamacher sum of each column.

For two vectors or matrices of identical dimensions, or for one scalar and one vector or matrix argument, return the pairwise Hamacher sum.

See also: algebraic_product, algebraic_sum, bounded_difference, bounded_sum, drastic_product, drastic_sum, einstein_product, einstein_sum, hamacher_product

fuzzy-logic-toolkit-0.6.1/docs/heart_disease_demo_1.html000066400000000000000000000106441466512601400233370ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: heart_disease_demo_1

Function Reference: heart_disease_demo_1

Script File: heart_disease_demo_1

Demonstrate the use of newfis, addvar, addmf, and addrule to build and evaluate an FIS. Also demonstrate the use of the algebraic product and sum as the T-norm/S-norm pair, and demonstrate the use of hedges in the FIS rules.

The demo:

  • builds an FIS
  • plots the input membership functions
  • plots the constant output functions
  • displays the FIS rules in verbose format in the Octave window
  • plots the FIS output as a function of the inputs

See also: cubic_approx_demo, heart_disease_demo_2, investment_portfolio_demo, linear_tip_demo, mamdani_tip_demo, sugeno_tip_demo

fuzzy-logic-toolkit-0.6.1/docs/heart_disease_demo_2.html000066400000000000000000000104701466512601400233350ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: heart_disease_demo_2

Function Reference: heart_disease_demo_2

Script File: heart_disease_demo_2

Demonstrate the use of the Octave Fuzzy Logic Toolkit to read and evaluate a Sugeno-type FIS stored in a file.

The demo:

  • reads the FIS structure from a file
  • plots the input membership functions
  • plots the (constant) output functions
  • plots the FIS output as a function of the inputs
  • evaluates the Sugeno-type FIS for four inputs

See also: cubic_approx_demo, heart_disease_demo_1, investment_portfolio_demo, linear_tip_demo, mamdani_tip_demo, sugeno_tip_demo

fuzzy-logic-toolkit-0.6.1/docs/index.html000066400000000000000000000554151466512601400204270ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit
fuzzy-logic-toolkit

fuzzy-logic-toolkit

0.6.1 2024-08-31

A mostly MATLAB-compatible fuzzy logic toolkit for Octave.

Select Category:

Evaluation

defuzz For a given domain, set of fuzzy function values, and defuzzification method, return the defuzzified (crisp) value of the fuzzy function.
evalfis Return the crisp output(s) of an FIS for each row in a matrix of crisp input values.
evalmf For a given domain, set of parameters, membership function type, and optional hedge and not_flag, return the corresponding y-values for the membership function.

Plotting

gensurf Generate and plot a surface (or 2-dimensional curve) showing one FIS output as a function of two (or one) of the FIS inputs.
plotmf Plot the membership functions defined for the specified FIS input or output variable on a single set of axes.

File Input/Output of Fuzzy Inference Systems

readfis Read the information in an FIS file, and using this information, create and return an FIS structure.
writefis Save the specified FIS currently in the Octave workspace to a file named by the user.

Command-Line Creation and Modification of Fuzzy Inference Systems

addmf Add a membership function to an existing FIS structure and return the updated FIS.
addrule Add a list of rules to an existing FIS structure and return the updated FIS.
addvar Add an input or output variable to an existing FIS structure and return the updated FIS.
newfis Create and return a new FIS structure using the argument values provided.
rmmf Remove a membership function from an existing FIS structure and return the updated FIS.
rmvar Remove an input or output variable from an existing FIS structure and return the updated FIS.
setfis Set a property (field) value of an FIS structure and return the updated FIS.

Text Representation of Fuzzy Inference Systems

getfis Return or print the property (field) values of an FIS structure specified by the arguments.
showfis Print all of the property (field) values of the FIS structure and its substructures.
showrule Show the rules for an FIS structure in verbose, symbolic, or indexed format.

Membership Functions

dsigmf For a given domain X and parameters PARAMS (or [A1 C1 A2 C2]), return the corresponding Y values for the difference between two sigmoidal membership functions.
gauss2mf For a given domain X and parameters PARAMS (or [SIG1 C1 SIG2 C2]), return the corresponding Y values for the two-sided Gaussian composite membership function.
gaussmf For a given domain X and parameters PARAMS (or [SIG C]), return the corresponding Y values for the Gaussian membership function.
gbellmf For a given domain X and parameters PARAMS (or [A B C]), return the corresponding Y values for the generalized bell-shaped membership function.
pimf For a given domain X and parameters PARAMS (or [A B C D]), return the corresponding Y values for the pi-shaped membership function.
psigmf For a given domain X and parameters PARAMS (or [A1 C1 A2 C2]), return the corresponding Y values for the product of two sigmoidal membership functions.
sigmf For a given domain X and parameters PARAMS (or [A C]), return the corresponding Y values for the sigmoidal membership function.
smf For a given domain X and parameters PARAMS (or [A B]), return the corresponding Y values for the S-shaped membership function.
trapmf For a given domain X and parameters PARAMS (or [A B C D]), return the corresponding Y values for the trapezoidal membership function.
trimf For a given domain X and parameters PARAMS (or [A B C]), return the corresponding Y values for the triangular membership function.
zmf For a given domain X and parameters PARAMS (or [A B]), return the corresponding Y values for the Z-shaped membership function.

T-Norms and S-Norms (in addition to max/min)

algebraic_product Return the algebraic product of the input.
algebraic_sum Return the algebraic sum of the input.
bounded_difference Return the bounded difference of the input.
bounded_sum Return the bounded sum of the input.
drastic_product Return the drastic product of the input.
drastic_sum Return the drastic sum of the input.
einstein_product Return the Einstein product of the input.
einstein_sum Return the Einstein sum of the input.
hamacher_product Return the Hamacher product of the input.
hamacher_sum Return the Hamacher sum of the input.

Complete Fuzzy Inference System Demos

cubic_approx_demo Demonstrate the use of the Octave Fuzzy Logic Toolkit to approximate a non-linear function using a Sugeno-type FIS with linear output functions.
heart_disease_demo_1 Demonstrate the use of newfis, addvar, addmf, and addrule to build and evaluate an FIS.
heart_disease_demo_2 Demonstrate the use of the Octave Fuzzy Logic Toolkit to read and evaluate a Sugeno-type FIS stored in a file.
investment_portfolio_demo Demonstrate the use of the Octave Fuzzy Logic Toolkit to read and evaluate a Mamdani-type FIS stored in a file.
linear_tip_demo Demonstrate the use of linear output membership functions to simulate constant membership functions.
mamdani_tip_demo Demonstrate the use of the Octave Fuzzy Logic Toolkit to read and evaluate a Mamdani-type FIS stored in a file.
sugeno_tip_demo Demonstrate the use of the Octave Fuzzy Logic Toolkit to read and evaluate a Sugeno-type FIS with multiple outputs stored in a text file.

Fuzzy Clustering Functions

fcm Using the Fuzzy C-Means algorithm, calculate and return the soft partition of a set of unlabeled data points.
gustafson_kessel Using the Gustafson-Kessel algorithm, calculate and return the soft partition of a set of unlabeled data points.
partition_coeff Return the partition coefficient for a given soft partition.
partition_entropy Return the partition entropy for a given soft partition.
xie_beni_index Return the Xie-Beni validity index for a given soft partition.
fuzzy-logic-toolkit-0.6.1/docs/investment_portfolio_demo.html000066400000000000000000000112611466512601400246040ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: investment_portfolio_demo

Function Reference: investment_portfolio_demo

Script File: investment_portfolio_demo

Demonstrate the use of the Octave Fuzzy Logic Toolkit to read and evaluate a Mamdani-type FIS stored in a file. Also demonstrate the use of hedges and weights in the FIS rules, the use of the Einstein product and sum as the T-norm/S-norm pair, and the non-standard use of the Einstein sum as the aggregation method.

The demo:

  • reads the FIS structure from a file
  • plots the input and output membership functions
  • plots the FIS output as a function of the inputs
  • plots the output of the 4 individual rules for (Age, Risk-Tolerance) = (40, 7)
  • plots the aggregated fuzzy output and the crisp output for (Age, Risk-Tolerance) = (40, 7)
  • shows the rules in verbose format in the Octave window

See also: cubic_approx_demo, heart_disease_demo_1, heart_disease_demo_2, linear_tip_demo, mamdani_tip_demo, sugeno_tip_demo

fuzzy-logic-toolkit-0.6.1/docs/linear_tip_demo.html000066400000000000000000000103661466512601400224460ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: linear_tip_demo

Function Reference: linear_tip_demo

Script File: linear_tip_demo

Demonstrate the use of linear output membership functions to simulate constant membership functions.

The demo:

  • reads the FIS structure from a file
  • plots the input membership functions
  • plots the FIS output as a function of the inputs
  • evaluates the Sugeno-type FIS for six inputs

See also: cubic_approx_demo, heart_disease_demo_1, heart_disease_demo_2, investment_portfolio_demo, mamdani_tip_demo, sugeno_tip_demo

fuzzy-logic-toolkit-0.6.1/docs/mamdani_tip_demo.html000066400000000000000000000107601466512601400226000ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: mamdani_tip_demo

Function Reference: mamdani_tip_demo

Script File: mamdani_tip_demo

Demonstrate the use of the Octave Fuzzy Logic Toolkit to read and evaluate a Mamdani-type FIS stored in a file.

The demo:

  • reads the FIS structure from a file
  • plots the input and output membership functions
  • plots each of the two FIS outputs as a function of the inputs
  • plots the output of the 4 individual rules for (Food-Quality, Service) = (4, 6)
  • plots the aggregated fuzzy output and the crisp output for (Food-Quality, Service) = (4, 6)
  • displays the FIS rules in symbolic format in the Octave window

See also: cubic_approx_demo, heart_disease_demo_1, heart_disease_demo_2, investment_portfolio_demo, linear_tip_demo, sugeno_tip_demo

fuzzy-logic-toolkit-0.6.1/docs/newfis.html000066400000000000000000000136431466512601400206100ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: newfis

Function Reference: newfis

Function File: a = newfis (fis_name)
Function File: a = newfis (fis_name, fis_type)
Function File: a = newfis (fis_name, fis_type, and_method)
Function File: a = newfis (fis_name, fis_type, and_method, or_method)
Function File: a = newfis (fis_name, fis_type, and_method, or_method, imp_method)
Function File: a = newfis (fis_name, fis_type, and_method, or_method, imp_method, agg_method)
Function File: a = newfis (fis_name, fis_type, and_method, or_method, imp_method, agg_method, defuzz_method)
Function File: a = newfis (fis_name, fis_type, and_method, or_method, imp_method, agg_method, defuzz_method, fis_version)

Create and return a new FIS structure using the argument values provided. Only the first argument is required. If fewer than eight arguments are given, then some or all of the following default values will be used:

ArgumentDefault Value
fis_type’mamdani’
and_method’min’
or_method’max’
imp_method’min’
agg_method’max’
defuzz_method’centroid’
fis_version1.0

See also: addmf, addrule, addvar, setfis

fuzzy-logic-toolkit-0.6.1/docs/partition_coeff.html000066400000000000000000000106721466512601400224670ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: partition_coeff

Function Reference: partition_coeff

Function File: vpc = partition_coeff (soft_partition)

Return the partition coefficient for a given soft partition.

The argument to partition_coeff is:

  • soft_partition: the membership degree of each input data point in each cluster

The return value is:

  • vpc: the partition coefficient for the given soft partition

To run demonstration code that uses this function, type "demo fcm" or "demo gustafson_kessel" (without the quotation marks) at the Octave prompt.

For more information about the soft_partition matrix, please see the documentation for function fcm.

See also: fcm, gustafson_kessel, partition_entropy, xie_beni_index

fuzzy-logic-toolkit-0.6.1/docs/partition_entropy.html000066400000000000000000000111711466512601400231000ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: partition_entropy

Function Reference: partition_entropy

Function File: vpe = partition_entropy (soft_partition, a)

Return the partition entropy for a given soft partition.

The arguments to partition_entropy are:

  • soft_partition: the membership degree of each input data point in each cluster
  • a: the log base to use in the calculation; must be a real number a > 1

The return value is:

  • vpe: the partition entropy for the given soft partition

To run demonstration code that uses this function, type "demo fcm" or "demo gustafson_kessel" (without the quotation marks) at the Octave prompt.

For more information about the soft_partition matrix, please see the For more information about the soft_partition matrix, please see the documentation for function fcm.

See also: fcm, gustafson_kessel, partition_coeff, xie_beni_index

fuzzy-logic-toolkit-0.6.1/docs/pimf.html000066400000000000000000000151731466512601400202500ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: pimf

Function Reference: pimf

Function File: y = pimf (x, params)
Function File: y = pimf ([x1 x2 ... xn], [a b c d])

For a given domain x and parameters params (or [a b c d]), return the corresponding y values for the pi-shaped membership function.

The argument x must be a real number or a non-empty vector of real numbers, and a, b, c, and d must be real numbers, with a < b <= c < d. This membership function satisfies: 

           0                             if x <= a
           2 * ((x - a)/(b - a))^2       if a < x <= (a + b)/2
           1 - 2 * ((x - b)/(b - a))^2   if (a + b)/2 < x < b
   f(x) =  1                             if b <= x <= c
           1 - 2 * ((x - c)/(d - c))^2   if c < x <= (c + d)/2
           2 * ((x - d)/(d - c))^2       if (c + d)/2 < x < d
           0                             if x >= d

which always returns values in the range [0, 1].

To run the demonstration code, type "demo pimf" (without the quotation marks) at the Octave prompt.

See also: dsigmf, gauss2mf, gaussmf, gbellmf, psigmf, sigmf, smf, trapmf, trimf, zmf

Example: 1

  

 x = 0:255;
 params = [70 80 100 140];
 y1 = pimf(x, params);
 params = [50 75 105 175];
 y2 = pimf(x, params);
 params = [30 70 110 200];
 y3 = pimf(x, params);
 figure('NumberTitle', 'off', 'Name', 'pimf demo');
 plot(x, y1, 'r;params = [70 80 100 140];', 'LineWidth', 2)
 hold on;
 plot(x, y2, 'b;params = [50 75 105 175];', 'LineWidth', 2)
 hold on;
 plot(x, y3, 'g;params = [30 70 110 200];', 'LineWidth', 2)
 ylim([-0.1 1.1]);
 xlabel('Crisp Input Value', 'FontWeight', 'bold');
 ylabel('Degree of Membership', 'FontWeight', 'bold');
 grid;
plotted figure

fuzzy-logic-toolkit-0.6.1/docs/plotmf.html000066400000000000000000000136761466512601400206240ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: plotmf

Function Reference: plotmf

Function File: plotmf (fis, in_or_out, var_index)
Function File: plotmf (fis, in_or_out, var_index, y_lower_limit)
Function File: plotmf (fis, in_or_out, var_index, y_lower_limit, y_upper_limit)

Plot the membership functions defined for the specified FIS input or output variable on a single set of axes. Fuzzy output membership functions are represented by the [0, 1]-valued fuzzy functions, and constant output membership functions are represented by unit-valued singleton spikes. Linear output membership functions, however, are represented by two-dimensional lines y = ax + c, regardless of how many dimensions the linear function is defined to have. In effect, all of the other dimensions of the linear function are set to 0.

If both constant and linear membership functions are used for a single FIS output, then two sets of axes are used: one for the constant membership functions, and another for the linear membership functions. To plot both constant and linear membership functions together, or to plot constant membership functions as horizontal lines instead of unit-valued spikes, represent the constant membership functions using ’linear’ functions, with 0 for all except the last parameter, and with the desired constant value as the last parameter.

The types/values of the arguments are expected to be:

ArgumentExpected Type or Value
fisan FIS structure
in_or_outeither ’input’ or ’output’ (case-insensitive)
var_indexan FIS input or output variable index
y_lower_limita real scalar (default value = -0.1)
y_upper_limita real scalar (default value = 1.1)

Six examples that use plotmf are:

  • cubic_approx_demo.m
  • heart_disease_demo_1.m
  • heart_disease_demo_2.m
  • investment_portfolio_demo.m
  • linear_tip_demo.m
  • mamdani_tip_demo.m
  • sugeno_tip_demo.m

See also: gensurf

fuzzy-logic-toolkit-0.6.1/docs/psigmf.html000066400000000000000000000154771466512601400206110ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: psigmf

Function Reference: psigmf

Function File: y = psigmf (x, params)
Function File: y = psigmf ([x1 x2 ... xn], [a1 c1 a2 c2])

For a given domain x and parameters params (or [a1 c1 a2 c2]), return the corresponding y values for the product of two sigmoidal membership functions.

The argument x must be a real number or a non-empty vector of strictly increasing real numbers, and a1, c1, a2, and c2 must be real numbers. This membership function satisfies the equation: 

     f(x) = (1/(1 + exp(-a1*(x - c1)))) * (1/(1 + exp(-a2*(x - c2))))

The function is bounded above by 1 and below by 0.

If a1 is positive, a2 is negative, and c1 and c2 are far enough apart with c1 < c2, then: 

     (a1)/4 ~ the rising slope at c1
         c1 ~ the left inflection point
     (a2)/4 ~ the falling slope at c2
         c2 ~ the right inflection point

and at each inflection point, the value of the function is about 0.5: 

      f(c1) ~ f(c2) ~ 0.5.

(Here, the symbol ~ means "approximately equal".)

To run the demonstration code, type "demo psigmf" (without the quotation marks) at the Octave prompt.

See also: dsigmf, gauss2mf, gaussmf, gbellmf, pimf, sigmf, smf, trapmf, trimf, zmf

Example: 1

  

 x = 0:100;
 params = [0.5 20 -0.3 60];
 y1 = psigmf(x, params);
 params = [0.3 20 -0.2 60];
 y2 = psigmf(x, params);
 params = [0.2 20 -0.1 60];
 y3 = psigmf(x, params);
 figure('NumberTitle', 'off', 'Name', 'psigmf demo');
 plot(x, y1, 'r;params = [0.5 20 -0.3 60];', 'LineWidth', 2)
 hold on;
 plot(x, y2, 'b;params = [0.3 20 -0.2 60];', 'LineWidth', 2)
 hold on;
 plot(x, y3, 'g;params = [0.2 20 -0.1 60];', 'LineWidth', 2)
 ylim([-0.1 1.1]);
 xlabel('Crisp Input Value', 'FontWeight', 'bold');
 ylabel('Degree of Membership', 'FontWeight', 'bold');
 grid;
plotted figure

fuzzy-logic-toolkit-0.6.1/docs/readfis.html000066400000000000000000000115521466512601400207270ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: readfis

Function Reference: readfis

Function File: fis = readfis ()
Function File: fis = readfis (filename)

Read the information in an FIS file, and using this information, create and return an FIS structure. If called without any arguments or with an empty string as an argument, present the user with a file dialog GUI. If called with a filename that does not end with ’.fis’, append ’.fis’ to the filename. The filename is expected to be a string.

Six examples of the input file format and example scripts that use readfis:

Example FIS FileCorresponding Example Script
cubic_approximator.fiscubic_approx_demo.m
heart_disease_risk.fisheart_disease_demo_2.m
investment_portfolio.fisinvestment_portfolio_demo.m
linear_tip_calculator.fislinear_tip_demo.m
mamdani_tip_calculator.fismamdani_tip_demo.m
sugeno_tip_calculator.fissugeno_tip_demo.m

See also: writefis

fuzzy-logic-toolkit-0.6.1/docs/rmmf.html000066400000000000000000000111761466512601400202550ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: rmmf

Function Reference: rmmf

Function File: fis = rmmf (fis, in_or_out, var_index, mf, mf_index)

Remove a membership function from an existing FIS structure and return the updated FIS.

The types/values of the arguments are expected to be:

ArgumentExpected Type or Value
fisan FIS structure
in_or_out’input’ or ’output’ (case-insensitive)
var_indexvalid index of an FIS input/output variable
mfthe string ’mf’
mf_indexan integer

Note that rmmf will allow the user to delete membership functions that are currently in use by rules in the FIS.

See also: addmf, rmvar

fuzzy-logic-toolkit-0.6.1/docs/rmvar.html000066400000000000000000000106761466512601400204470ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: rmvar

Function Reference: rmvar

Function File: fis = rmvar (fis, in_or_out, var_index)

Remove an input or output variable from an existing FIS structure and return the updated FIS.

The types/values of the arguments are expected to be:

ArgumentExpected Type or Value
fisan FIS structure
in_or_outeither ’input’ or ’output’ (case-insensitive)
var_indexan FIS input or output variable index

Note that rmvar will allow the user to delete an input or output variable that is currently in use by rules in the FIS.

See also: addvar, rmmf

fuzzy-logic-toolkit-0.6.1/docs/setfis.html000066400000000000000000000156041466512601400206110ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: setfis

Function Reference: setfis

Function File: fis = setfis (fis, property, property_value)
Function File: fis = setfis (fis, in_or_out, var_index, var_property, var_property_value)
Function File: fis = setfis (fis, in_or_out, var_index, mf, mf_index, mf_property, mf_property_value)

Set a property (field) value of an FIS structure and return the updated FIS.

There are three forms of setfis:

Number of ArgumentsAction Taken
3Set a property of the FIS structure. The properties that may be set are: name, type, andmethod, ormethod, impmethod, addmethod, defuzzmethod, and version.
5Set a property of an input or output variable of the FIS structure. The properties that may be set are: name and range.
7Set a property of a membership function. The properties that may be set are: name, type, and params.

The types/values of the arguments are expected to be:

ArgumentExpected Type or Value
fisan FIS structure
propertya string; one of ’name’, ’type’, ’andmethod’, ’ormethod’, ’impmethod’, ’addmethod’, ’defuzzmethod’, and ’version’ (case-insensitive)
property_valuea number (if property is ’version’); a string (otherwise)
in_or_outeither ’input’ or ’output’ (case-insensitive)
var_indexa valid integer index of an input or output FIS variable
var_propertya string; either ’name’ or ’range’
var_property_valuea string (if var_property is ’name’) or a vector range (if var_property is ’range’)
mfthe string ’mf’
mf_indexa valid integer index of a membership function
mf_propertya string; one of ’name’, ’type’, or ’params’
mf_property_valuea string (if mf_property is ’name’ or ’type’); an array (if mf_property is ’params’)

Note that all of the strings representing properties above are case insensitive.

See also: newfis, getfis, showfis

fuzzy-logic-toolkit-0.6.1/docs/showfis.html000066400000000000000000000073321466512601400207750ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: showfis

Function Reference: showfis

Function File: showfis (fis)

Print all of the property (field) values of the FIS structure and its substructures.

See also: getfis, showrule

fuzzy-logic-toolkit-0.6.1/docs/showrule.html000066400000000000000000000263061466512601400211650ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: showrule

Function Reference: showrule

Function File: showrule (fis)
Function File: showrule (fis, index_list)
Function File: showrule (fis, index_list, format)
Function File: showrule (fis, index_list, 'verbose', language)
Function File: showrule (fis, index_list, 'verbose', 'custom', {"and" "or" "If" "then" "is" "isn't" "somewhat" "very" "extremely" "very very"})

Show the rules for an FIS structure in verbose, symbolic, or indexed format. Built in languages for the ’verbose’ format are: English, Chinese (or Mandarin, Pinyin), Russian (or Pycckii, Russkij), French (or Francais), Spanish (or Espanol), and German (or Deutsch). The names of the languages are case-insensitive, Chinese is written in Pinyin, and Russian is transliterated.

To use a custom language, enter ’verbose’ and ’custom’ for the third and fourth parameters, respectively, and a cell array of ten strings (to specify the custom language) corresponding to the English {"and" "or" "If" "then" "is" "isn’t" "somewhat" "very" "extremely" "very very"} for the fifth parameter.

To run the demonstration code, type "demo showrule" (without the quotation marks) at the Octave prompt.

See also: addrule, getfis, showfis

Example: 1

  

 fis = readfis ('sugeno_tip_calculator.fis');
 puts ("Output of: showrule(fis)\n");
 showrule (fis)
 puts ("\n");

Output of: showrule(fis)
1. If (Food-Quality is extremely Bad) and (Service is extremely Bad), then (Cheap-Tip is extremely Low) and (Average-Tip is very Low) and (Generous-Tip is Low) (1)
2. If (Food-Quality is Good) and (Service is extremely Bad), then (Cheap-Tip is Low) and (Average-Tip is Low) and (Generous-Tip is Medium) (1)
3. If (Food-Quality is very Good) and (Service is very Bad), then (Cheap-Tip is Low) and (Average-Tip is Medium) and (Generous-Tip is High) (1)
4. If (Food-Quality is Bad) and (Service is Bad), then (Cheap-Tip is Low) and (Average-Tip is Low) and (Generous-Tip is Medium) (1)
5. If (Food-Quality is Good) and (Service is Bad), then (Cheap-Tip is Low) and (Average-Tip is Medium) and (Generous-Tip is High) (1)
6. If (Food-Quality is extremely Good) and (Service is Bad), then (Cheap-Tip is Low) and (Average-Tip is Medium) and (Generous-Tip is very High) (1)
7. If (Food-Quality is Bad) and (Service is Good), then (Cheap-Tip is Low) and (Average-Tip is Medium) and (Generous-Tip is High) (1)
8. If (Food-Quality is Good) and (Service is Good), then (Cheap-Tip is Medium) and (Average-Tip is Medium) and (Generous-Tip is very High) (1)
9. If (Food-Quality is very Bad) and (Service is very Good), then (Cheap-Tip is Low) and (Average-Tip is Medium) and (Generous-Tip is High) (1)
10. If (Food-Quality is very very Good) and (Service is very very Good), then (Cheap-Tip is High) and (Average-Tip is very High) and (Generous-Tip is extremely High) (1)

Example: 2

  

 fis = readfis ('sugeno_tip_calculator.fis');
 puts ("Output of: showrule(fis, [2 4], 'symbolic')\n");
 showrule (fis, [2 4], 'symbolic')
 puts ("\n");

Output of: showrule(fis, [2 4], 'symbolic')
2.  (Food-Quality == Good) && (Service == Bad^3.0) => (Cheap-Tip == Low) && (Average-Tip == Low) && (Generous-Tip == Medium) (1)
4.  (Food-Quality == Bad) && (Service == Bad) => (Cheap-Tip == Low) && (Average-Tip == Low) && (Generous-Tip == Medium) (1)

Example: 3

  

 fis = readfis ('sugeno_tip_calculator.fis');
 puts ("Output of: showrule(fis, 1:4, 'indexed')\n");
 showrule (fis, 1:4, 'indexed')
 puts ("\n");

Output of: showrule(fis, 1:4, 'indexed')
1.30 1.30, 1.30 1.20 1 (1) : 1
2 1.30, 1 1 2 (1) : 1
2.20 1.20, 1 2 3 (1) : 1
1 1, 1 1 2 (1) : 1

Example: 4

  

 fis = readfis ('sugeno_tip_calculator.fis');
 puts ("Output of: showrule(fis, 1, 'verbose', 'francais')\n");
 showrule (fis, 1, 'verbose', 'francais')
 puts ("\n");

Output of: showrule(fis, 1, 'verbose', 'francais')
1. Si (Food-Quality est extremement Bad) et (Service est extremement Bad), alors (Cheap-Tip est extremement Low) et (Average-Tip est tres Low) et (Generous-Tip est Low) (1)
fuzzy-logic-toolkit-0.6.1/docs/sigmf.html000066400000000000000000000145511466512601400204210ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: sigmf

Function Reference: sigmf

Function File: y = sigmf (x, params)
Function File: y = sigmf ([x1 x2 ... xn], [a c])

For a given domain x and parameters params (or [a c]), return the corresponding y values for the sigmoidal membership function.

The argument x must be a real number or a non-empty vector of strictly increasing real numbers, and a and c must be real numbers. This membership function satisfies the equation: 

     f(x) = 1/(1 + exp(-a*(x - c)))

which always returns values in the range [0, 1].

The parameters a and c specify: 

     a == the slope at c
     c == the inflection point

and at the inflection point, the value of the function is 0.5: 

     f(c) == 0.5.

To run the demonstration code, type "demo sigmf" (without the quotation marks) at the Octave prompt.

See also: dsigmf, gauss2mf, gaussmf, gbellmf, pimf, psigmf, smf, trapmf, trimf, zmf

Example: 1

  

 x = 0:100;
 params = [0.3 40];
 y1 = sigmf(x, params);
 params = [0.2 40];
 y2 = sigmf(x, params);
 params = [0.1 40];
 y3 = sigmf(x, params);
 figure('NumberTitle', 'off', 'Name', 'sigmf demo');
 plot(x, y1, 'r;params = [0.3 40];', 'LineWidth', 2)
 hold on;
 plot(x, y2, 'b;params = [0.2 40];', 'LineWidth', 2)
 hold on;
 plot(x, y3, 'g;params = [0.1 40];', 'LineWidth', 2)
 ylim([-0.1 1.2]);
 xlabel('Crisp Input Value', 'FontWeight', 'bold');
 ylabel('Degree of Membership', 'FontWeight', 'bold');
 grid;
plotted figure

fuzzy-logic-toolkit-0.6.1/docs/smf.html000066400000000000000000000145171466512601400201030ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: smf

Function Reference: smf

Function File: y = smf (x, params)
Function File: y = smf ([x1 x2 ... xn], [a b])

For a given domain x and parameters params (or [a b]), return the corresponding y values for the S-shaped membership function.

The argument x must be a real number or a non-empty vector of strictly increasing real numbers, and a and b must be real numbers, with a < b. This membership function satisfies: 

           0                                if x <= a
   f(x) =  2 * ((x - a)/(b - a))^2          if a < x <= (a + b)/2
           1 - 2 * ((x - b)/(b - a))^2      if (a + b)/2 < x < b
           1                                if x >= b

which always returns values in the range [0, 1].

To run the demonstration code, type "demo smf" (without the quotation marks) at the Octave prompt.

See also: dsigmf, gauss2mf, gaussmf, gbellmf, pimf, psigmf, sigmf, trapmf, trimf, zmf

Example: 1

  

 x = 0:100;
 params = [40 60];
 y1 = smf(x, params);
 params = [25 75];
 y2 = smf(x, params);
 params = [10 90];
 y3 = smf(x, params);
 figure('NumberTitle', 'off', 'Name', 'smf demo');
 plot(x, y1, 'r;params = [40 60];', 'LineWidth', 2)
 hold on;
 plot(x, y2, 'b;params = [25 75];', 'LineWidth', 2)
 hold on;
 plot(x, y3, 'g;params = [10 90];', 'LineWidth', 2)
 ylim([-0.1 1.2]);
 xlabel('Crisp Input Value', 'FontWeight', 'bold');
 ylabel('Degree of Membership', 'FontWeight', 'bold');
 grid;
plotted figure

fuzzy-logic-toolkit-0.6.1/docs/sugeno_tip_demo.html000066400000000000000000000110301466512601400224610ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: sugeno_tip_demo

Function Reference: sugeno_tip_demo

Script File: sugeno_tip_demo

Demonstrate the use of the Octave Fuzzy Logic Toolkit to read and evaluate a Sugeno-type FIS with multiple outputs stored in a text file. Also demonstrate the use of hedges in the FIS rules and the Einstein product and sum as the T-norm/S-norm pair.

The demo:

  • reads the FIS structure from a file
  • plots the input membership functions
  • plots the (constant) output functions
  • plots each of the three FIS outputs as a function of the inputs
  • displays the FIS rules in verbose format in the Octave window
  • evaluates the Sugeno-type FIS for six inputs

See also: cubic_approx_demo, heart_disease_demo_1, heart_disease_demo_2, investment_portfolio_demo, linear_tip_demo, mamdani_tip_demo

fuzzy-logic-toolkit-0.6.1/docs/trapmf.html000066400000000000000000000151551466512601400206060ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: trapmf

Function Reference: trapmf

Function File: y = trapmf (x, params)
Function File: y = trapmf ([x1 x2 ... xn], [a b c d])

For a given domain x and parameters params (or [a b c d]), return the corresponding y values for the trapezoidal membership function.

The argument x must be a real number or a non-empty vector of strictly increasing real numbers, and parameters a, b, c, and d must satisfy the inequalities: a < b <= c < d. None of the parameters a, b, c, d are required to be in the domain x. The minimum and maximum values of the trapezoid are assumed to be 0 and 1.

The parameters [a b c d] correspond to the x values of the corners of the trapezoid: 

        1-|      --------
          |     /        \
          |    /          \
          |   /            \
        0-----------------------
             a   b      c   d

To run the demonstration code, type "demo trapmf" (without the quotation marks) at the Octave prompt.

See also: dsigmf, gauss2mf, gaussmf, gbellmf, pimf, psigmf, sigmf, smf, trimf, zmf

Example: 1

  

 x = 0:100;
 params = [-1 0 20 40];
 y1 = trapmf(x, params);
 params = [20 40 60 80];
 y2 = trapmf(x, params);
 params = [60 80 100 101];
 y3 = trapmf(x, params);
 figure('NumberTitle', 'off', 'Name', 'trapmf demo');
 plot(x, y1, 'r;params = [-1 0 20 40];', 'LineWidth', 2)
 hold on;
 plot(x, y2, 'b;params = [20 40 60 80];', 'LineWidth', 2)
 hold on;
 plot(x, y3, 'g;params = [60 80 100 101];', 'LineWidth', 2)
 ylim([-0.1 1.2]);
 xlabel('Crisp Input Value', 'FontWeight', 'bold');
 ylabel('Degree of Membership', 'FontWeight', 'bold');
 grid;
plotted figure

fuzzy-logic-toolkit-0.6.1/docs/trimf.html000066400000000000000000000150651466512601400204360ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: trimf

Function Reference: trimf

Function File: y = trimf (x, params)
Function File: y = trimf ([x1 x2 ... xn], [a b c])

For a given domain x and parameters params (or [a b c]), return the corresponding y values for the triangular membership function.

The argument x must be a real number or a non-empty vector of strictly increasing real numbers, and parameters a, b, and c must be real numbers that satisfy a < b < c. None of the parameters a, b, and c are required to be in the domain x. The minimum and maximum values of the triangle are assumed to be 0 and 1.

The parameters [a b c] correspond to the x values of the vertices of the triangle: 

        1-|         /\
          |        /  \
          |       /    \
          |      /      \
        0-----------------------
                a   b   c

To run the demonstration code, type "demo trimf" (without the quotation marks) at the Octave prompt.

See also: dsigmf, gauss2mf, gaussmf, gbellmf, pimf, psigmf, sigmf, smf, trapmf, trimf_demo, zmf

Example: 1

  

 x = 0:100;
 params = [-1 0 50];
 y1 = trimf(x, params);
 params = [0 50 100];
 y2 = trimf(x, params);
 params = [50 100 101];
 y3 = trimf(x, params);
 figure('NumberTitle', 'off', 'Name', 'trimf demo');
 plot(x, y1, 'r;params = [-1 0 50];', 'LineWidth', 2)
 hold on;
 plot(x, y2, 'b;params = [0 50 100];', 'LineWidth', 2)
 hold on;
 plot(x, y3, 'g;params = [50 100 101];', 'LineWidth', 2)
 ylim([-0.1 1.2]);
 xlabel('Crisp Input Value', 'FontWeight', 'bold');
 ylabel('Degree of Membership', 'FontWeight', 'bold');
 grid;
plotted figure

fuzzy-logic-toolkit-0.6.1/docs/writefis.html000066400000000000000000000131441466512601400211450ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: writefis

Function Reference: writefis

Function File: writefis (fis)
Function File: writefis (fis, filename)
Function File: writefis (fis, filename, dialog)

Save the specified FIS currently in the Octave workspace to a file named by the user.

There are three forms of writefis:

Number of ArgumentsAction Taken
1Open a dialog GUI to help the user choose a directory and name for the output file.
2Do not open a dialog GUI. Save the FIS to a file in the current directory with the specified filename. If the specified filename does not end in ’.fis’, append ’.fis’ to the filename.
3Open a dialog GUI with the specified filename in the ’filename’ textbox of the GUI. If the specified filename does not end in ’.fis’, append ’.fis’ to the filename.

The types/values of the arguments are expected to be:

ArgumentExpected Type or Value
fisan FIS structure satisfying is_fis (see private/is_fis.m)
filenamea string; if the string does not already end with the extension ".fis", then ".fis" is added
dialogthe string ’dialog’ (case insensitive)

Note: The GUI dialog requires zenity to be installed on the system.

Known error: When using the file dialog, if the user clicks "Cancel" instead of saving the file, an error message is generated.

See also: readfis

fuzzy-logic-toolkit-0.6.1/docs/xie_beni_index.html000066400000000000000000000113631466512601400222630ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: xie_beni_index

Function Reference: xie_beni_index

Function File: vxb = xie_beni_index (input_data, cluster_centers, soft_partition)

Return the Xie-Beni validity index for a given soft partition.

The arguments to xie_beni_index are:

  • input_data: a matrix of input data points; each row corresponds to one point
  • cluster_centers: a matrix of cluster centers; each row corresponds to one point
  • soft_partition: the membership degree of each input data point in each cluster

The return value is:

  • vxb: the Xie-Beni validity index for the given partition

To run demonstration code that uses this function, type "demo fcm" or "demo gustafson_kessel" (without the quotation marks) at the Octave prompt.

For more information about the input_data, cluster_centers, and soft_partition matrices, please see the documentation for function fcm.

See also: fcm, gustafson_kessel, partition_coeff, partition_entropy

fuzzy-logic-toolkit-0.6.1/docs/zmf.html000066400000000000000000000152051466512601400201050ustar00rootroot00000000000000 Octave Fuzzy Logic Toolkit: zmf

Function Reference: zmf

Function File: y = zmf (x, params)
Function File: y = zmf ([x1 x2 ... xn], [a b])

For a given domain x and parameters params (or [a b]), return the corresponding y values for the Z-shaped membership function.

The argument x must be a real number or a non-empty vector of strictly increasing real numbers, and a and b must be real numbers, with a < b. This membership function satisfies: 

             1                               if x <= a
     f(x) =  1 - 2 * ((x - a)/(b - a))^2     if a < x <= (a + b)/2
             2 * ((x - b)/(b - a))^2         if (a + b)/2 < x < b
             0                               if x >= b

which always returns values in the range [0, 1].

The parameters a and b specify: 

     a == the rightmost point at which f(x) = 1
     b == the leftmost point at which f(x) = 0

At the midpoint of the segment [a, b], the function value is 0.5: 

     f((a + b)/2) = 0.5

To run the demonstration code, type "demo zmf" (without the quotation marks) at the Octave prompt.

See also: dsigmf, gauss2mf, gaussmf, gbellmf, pimf, psigmf, sigmf, smf, trapmf, trimf, zmf_demo

Example: 1

  

 x = 0:100;
 params = [40 60];
 y1 = zmf(x, params);
 params = [25 75];
 y2 = zmf(x, params);
 params = [10 90];
 y3 = zmf(x, params);
 figure('NumberTitle', 'off', 'Name', 'zmf demo');
 plot(x, y1, 'r;params = [40 60];', 'LineWidth', 2)
 hold on;
 plot(x, y2, 'b;params = [25 75];', 'LineWidth', 2)
 hold on;
 plot(x, y3, 'g;params = [10 90];', 'LineWidth', 2)
 ylim([-0.1 1.1]);
 xlabel('Crisp Input Value', 'FontWeight', 'bold');
 ylabel('Degree of Membership', 'FontWeight', 'bold');
 grid;
plotted figure

fuzzy-logic-toolkit-0.6.1/inst/000077500000000000000000000000001466512601400164455ustar00rootroot00000000000000fuzzy-logic-toolkit-0.6.1/inst/addmf.m000066400000000000000000000147201466512601400177020ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{fis} =} addmf (@var{fis}, @var{in_or_out}, @var{var_index}, @var{mf_name}, @var{mf_type}, @var{mf_params}) ## ## Add a membership function to an existing FIS ## structure and return the updated FIS. ## ## The types/values of the arguments are expected to be: ## ## @multitable @columnfractions .35 .65 ## @headitem Argument @tab Expected Type or Value ## @item @var{fis} ## @tab an FIS structure ## @item @var{in_or_out} ## @tab 'input' or 'output' (case-insensitive) ## @item @var{var_index} ## @tab valid index of an FIS input/output variable ## @item @var{mf_name} ## @tab a string ## @item @var{mf_type} ## @tab a string ## @item @var{mf_params} ## @tab a vector ## @end multitable ## @sp 1 ## If @var{mf_type} is one of the built-in membership functions, then the ## number and values of the parameters must satisfy the membership function ## requirements for the specified @var{mf_type}. ## ## Note that addmf will allow the user to add membership functions or ## membership function names for a given input or output variable that ## duplicate mfs or mf names already entered. ## ## Also, constant and linear membership functions are not restricted to FIS ## structure outputs or to Sugeno-type FIS structures, and the result of using ## them for FIS inputs or Mamdani-type FIS outputs has not yet been tested. ## ## To run the demonstration code, type "@t{demo addmf}" (without the quotation ## marks) at the Octave prompt. ## This demo creates two FIS input variables and associated membership functions ## and then produces two figures showing the term sets for the two FIS inputs. ## ## @seealso{rmmf, setfis} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy membership ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: addmf.m ## Note: The demo code is based on an assignment written by ## Dr. Bruce Segee (University of Maine Dept. of ECE). ## Last-Modified: 12 Jun 2024 function fis = addmf (fis, in_or_out, var_index, mf_name, mf_type, ... mf_params) ## If the caller did not supply 6 argument values with the correct ## types, print an error message and halt. if (nargin != 6) error ("addmf requires 6 arguments\n"); elseif (!is_fis (fis)) error ("addmf's first argument must be an FIS structure\n"); elseif (!(is_string (in_or_out) && ... ismember (tolower (in_or_out), {'input', 'output'}))) error ("addmf's second argument must be 'input' or 'output'\n"); elseif (!is_var_index (fis, in_or_out, var_index)) error ("addmf's third argument must be a variable index\n"); elseif (!(is_string (mf_name) && is_string (mf_type))) error ("addmf's fourth and fifth arguments must be strings\n"); elseif (!are_mf_params (mf_type, mf_params)) error ("addmf's sixth argument must be a vector of parameters\n"); endif ## Create a new membership function struct and update the ## FIS structure. new_mf = struct ('name', mf_name, 'type', mf_type, 'params', ... mf_params); if (strcmp (tolower (in_or_out), 'input')) if (length (fis.input(var_index).mf) == 0) fis.input(var_index).mf = new_mf; else fis.input(var_index).mf = [fis.input(var_index).mf, new_mf]; endif else if (length (fis.output(var_index).mf) == 0) fis.output(var_index).mf = new_mf; else fis.output(var_index).mf = [fis.output(var_index).mf, new_mf]; endif endif endfunction %!demo %! ## Create new FIS. %! a = newfis ('Heart-Disease-Risk', 'sugeno', ... %! 'min', 'max', 'min', 'max', 'wtaver'); %! %! ## Add two inputs and their membership functions. %! a = addvar (a, 'input', 'LDL-Level', [0 300]); %! a = addmf (a, 'input', 1, 'Low', 'trapmf', [-1 0 90 110]); %! a = addmf (a, 'input', 1, 'Low-Borderline', 'trapmf', ... %! [90 110 120 140]); %! a = addmf (a, 'input', 1, 'Borderline', 'trapmf', ... %! [120 140 150 170]); %! a = addmf (a, 'input', 1, 'High-Borderline', 'trapmf', ... %! [150 170 180 200]); %! a = addmf (a, 'input', 1, 'High', 'trapmf', [180 200 300 301]); %! %! a = addvar (a, 'input', 'HDL-Level', [0 100]); %! a = addmf (a, 'input', 2, 'Low-HDL', 'trapmf', [-1 0 35 45]); %! a = addmf (a, 'input', 2, 'Moderate-HDL', 'trapmf', [35 45 55 65]); %! a = addmf (a, 'input', 2, 'High-HDL', 'trapmf', [55 65 100 101]); %! %! ## Plot the input membership functions. %! plotmf (a, 'input', 1); %! plotmf (a, 'input', 2); %!shared fis %! fis = readfis ('mamdani_tip_calculator.fis'); %!test %! fis = addmf(fis, 'input', 1, 'Excellent', 'trapmf', [5 8 10 11]); %! assert(fis.input(1).mf(3).name, 'Excellent'); ## Test input validation %!error %! addmf() %!error %! addmf(1) %!error %! addmf(1, 2) %!error %! addmf(1, 2, 3) %!error %! addmf(1, 2, 3, 4) %!error %! addmf(1, 2, 3, 4, 5) %!error %! addmf(1, 2, 3, 4, 5, 6, 7) %!error %! addmf(1, 2, 3, 4, 5, 6) %!error %! addmf(fis, 'file', 3, 4, 5, 6) %!error %! addmf(fis, 'input', 3, 4, 5, 6) %!error %! addmf(fis, 'input', 1, 4, 'string', 6) %!error %! addmf(fis, 'input', 1, 'string', 5, 6) %!error %! addmf(fis, 'input', 1, 'string', 'trapmf', []) fuzzy-logic-toolkit-0.6.1/inst/addrule.m000066400000000000000000000113411466512601400202430ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{fis} =} addrule (@var{fis}, @var{rule_matrix}) ## ## Add a list of rules to an existing FIS structure and return ## the updated FIS. ## ## Each row of the @var{rule_matrix} represents one rule and has the form: ## ## @verbatim ## [in1_mf ... inM_mf out1_mf ... outN_mf weight connect] ## @end verbatim ## ## where: ## ## @multitable @columnfractions .25 .70 ## @headitem Element in Rule Vector @tab Expected Type or Value ## @item in_mf ## @tab membership function index for input i ## @item out_mf ## @tab membership function index for output j ## @item weight ## @tab relative weight of the rule (0 <= weight <= 1) ## @item connect ## @tab antecedent connective (1 == and; 2 == or) ## @item @ @ ## @tab @ @ ## @headitem Hedge String @tab Effect of Applying Hedge ## @item "not" ## @tab prepend a minus sign to the membership function index ## @item "somewhat" ## @tab append ".05" to the membership function index ## @item "very" ## @tab append ".20" to the membership function index ## @item "extremely" ## @tab append ".30" to the membership function index ## @item "very very" ## @tab append ".40" to the membership function index ## @item custom hedge ## @tab append .xy, where x.y is the degree to which the membership ## value should be raised, to the membership function index ## @end multitable ## @sp 1 ## To omit an input or output, use 0 for the membership function index. ## The consequent connective is always "and". ## ## For example, to express: ## ## @verbatim ## "If (input_1 is mf_2) or (input_3 is not mf_1) or (input_4 is very mf_1), ## then (output_1 is mf_2) and (output_2 is mf_1^0.3)." ## @end verbatim ## ## with weight 1, the corresponding row of @var{rule_matrix} would be: ## ## @verbatim ## [2 0 -1 4.2 2 1.03 1 2] ## @end verbatim ## ## For a complete example that uses addrule, see heart_disease_demo_1.m. ## ## @seealso{heart_disease_demo_1, showrule} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy rule ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: addrule.m ## Last-Modified: 13 Jun 2024 function fis = addrule (fis, rule_matrix) ## If the caller did not supply 2 argument values with the correct ## types, print an error message and halt. if (nargin != 2) error ("addrule requires 2 arguments\n"); elseif (!is_fis (fis)) error ("addrule's first argument must be an FIS structure\n"); elseif (!is_real_matrix (rule_matrix)) error ("addrule's second argument must be a matrix of real numbers\n"); endif ## For each row in the rule_matrix, create a new rule struct and ## update the FIS structure. num_inputs = columns (fis.input); num_outputs = columns (fis.output); for i = 1 : rows (rule_matrix) antecedent = rule_matrix(i, 1 : num_inputs); consequent = rule_matrix(i, ... (num_inputs+1) : (num_inputs+num_outputs)); weight = rule_matrix(i, num_inputs + num_outputs + 1); connection = rule_matrix(i, num_inputs + num_outputs + 2); new_rules(i) = struct ('antecedent', antecedent, ... 'consequent', consequent, ... 'weight', weight, ... 'connection', connection); endfor if (length (fis.rule) == 0) fis.rule = new_rules; else fis.rule = [fis.rule, new_rules]; endif endfunction %!shared fis %! fis = readfis ('mamdani_tip_calculator.fis'); %!test %! fis = addrule(fis, [1 2 2 1 1 1]); %! assert(fis.rule(5).antecedent, [1 2]); ## Test input validation %!error %! addrule() %!error %! addrule(1) %!error %! addrule(1, 2, 3) %!error %! addrule(1, 2) %!error %! addrule(fis, 2j) fuzzy-logic-toolkit-0.6.1/inst/addvar.m000066400000000000000000000101601466512601400200620ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{fis} =} addvar (@var{fis}, @var{in_or_out}, @var{var_name}, @var{var_range}) ## ## Add an input or output variable to an existing FIS ## structure and return the updated FIS. ## ## The types/values of the arguments are expected to be: ## ## @multitable @columnfractions .35 .40 ## @headitem Argument @tab Expected Type or Value ## @item @var{fis} ## @tab an FIS structure ## @item @var{in_or_out} ## @tab either 'input' or 'output' (case-insensitive) ## @item @var{var_name} ## @tab a string ## @item @var{var_range} ## @tab a vector [x1 x2] of two real numbers ## @end multitable ## @sp 1 ## The vector components x1 and x2, which must also satisfy x1 <= x2, ## specify the lower and upper bounds of the variable's domain. ## ## To run the demonstration code, type "@t{demo addvar}" (without the quotation ## marks) at the Octave prompt. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy variable ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: addvar.m ## Last-Modified: 13 Jun 2024 function fis = addvar (fis, in_or_out, var_name, var_range) ## If the caller did not supply 4 argument values with the correct ## types, print an error message and halt. if (nargin != 4) error ("addvar requires 4 arguments\n"); elseif (!is_fis (fis)) error ("addvar's first argument must be an FIS structure\n"); elseif (!(is_string (in_or_out) && ... ismember (tolower (in_or_out), {'input', 'output'}))) error ("addvar's second argument must be 'input' or 'output'\n"); elseif (!is_string (var_name)) error ("addvar's third argument must be a string\n"); elseif (!are_bounds (var_range)) error ("addvar's fourth argument must specify variable bounds\n"); endif ## Create a new variable struct and update the FIS input or output ## variable list. new_variable = struct ('name', var_name, 'range', var_range, ... 'mf', []); if (strcmp (tolower (in_or_out), 'input')) if (length (fis.input) == 0) fis.input = new_variable; else fis.input = [fis.input, new_variable]; endif else if (length (fis.output) == 0) fis.output = new_variable; else fis.output = [fis.output, new_variable]; endif endif endfunction %!demo %! a = newfis ('Heart-Disease-Risk', 'sugeno', ... %! 'min', 'max', 'min', 'max', 'wtaver'); %! a = addvar (a, 'input', 'LDL-Level', [0 300]); %! getfis (a, 'input', 1); %!shared fis %! fis = readfis ('mamdani_tip_calculator.fis'); %!test %! fis = addvar(fis, 'input', 'Dining-Room', [1 10]); %! assert(fis.input(3).name == 'Dining-Room'); ## Test input validation %!error %! addvar() %!error %! addvar(1) %!error %! addvar(1, 2) %!error %! addvar(1, 2, 3) %!error %! addvar(1, 2, 3, 4, 5) %!error %! addvar(1, 2, 3, 4) %!error %! addvar(fis, 2, 3, 4) %!error %! addvar(fis, 'input', 3, 4) %!error %! addvar(fis, 'input', 'string', 4) fuzzy-logic-toolkit-0.6.1/inst/algebraic_product.m000066400000000000000000000065231466512601400223020ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{retval} =} algebraic_product (@var{x}) ## @deftypefnx {Function File} {@var{retval} =} algebraic_product (@var{x}, @var{y}) ## ## Return the algebraic product of the input. ## The algebraic product of two real scalars x and y is: x * y ## ## For one vector argument, apply the algebraic product to all of elements of ## the vector. (The algebraic product is associative.) For one two-dimensional ## matrix argument, return a vector of the algebraic product of each column. ## ## For two vectors or matrices of identical dimensions, or for one scalar and ## one vector or matrix argument, return the pairwise product. ## ## @seealso{algebraic_sum, bounded_difference, bounded_sum, drastic_product, drastic_sum, einstein_product, einstein_sum, hamacher_product, hamacher_sum} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy algebraic_product ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: algebraic_product.m ## Last-Modified: 26 Jul 2024 function retval = algebraic_product (x, y = 0) if ((nargin != 1) && (nargin != 2)) error ("algebraic_product requires 1 or 2 arguments\n"); elseif (!(isreal (x) && isreal (y))) error ("arguments to algebraic_product must be real scalars or matrices\n"); elseif (nargin == 2 && ... (isscalar (x) || isscalar (y) || ... isequal (size (x), size (y)))) retval = x .* y; elseif (nargin == 1 && ndims (x) <= 2) retval = prod (x); else error ("invalid arguments to function algebraic_product\n"); endif endfunction %!test %! x = [5 2 3 6]; %! z = algebraic_product(x); %! assert(z, 180); %!test %! x = [5 2 3 6]; %! y = [-1 0 2 3]; %! z = algebraic_product(x, y); %! assert(z, [-5 0 6 18]); ## Test input validation %!error %! algebraic_product() %!error %! algebraic_product(1, 2, 3) %!error %! algebraic_product(2j) %!error %! algebraic_product(1, 2j) %!error %! algebraic_product([1 2j]) %!error %! algebraic_product([1 2], [1 2 3]) %!error %! algebraic_product([1 2], [1 2; 3 4]) %!error %! algebraic_product(0:100, []) fuzzy-logic-toolkit-0.6.1/inst/algebraic_sum.m000066400000000000000000000071361466512601400214270ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{retval} =} algebraic_sum (@var{x, y}) ## @deftypefnx {Function File} {@var{retval} =} algebraic_sum (@var{x, y}) ## ## Return the algebraic sum of the input. ## The algebraic sum of two real scalars x and y is: x + y - x * y ## ## For one vector argument, apply the algebraic sum to all of elements of ## the vector. (The algebraic sum is associative.) For one two-dimensional ## matrix argument, return a vector of the algebraic sum of each column. ## ## For two vectors or matrices of identical dimensions, or for one scalar and ## one vector or matrix argument, return the pairwise algebraic sum. ## ## @seealso{algebraic_product, bounded_difference, bounded_sum, drastic_product, drastic_sum, einstein_product, einstein_sum, hamacher_product, hamacher_sum} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy algebraic_sum ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: algebraic_sum.m ## Last-Modified: 26 Jul 2024 function retval = algebraic_sum (x, y = 0) if ((nargin != 1) && (nargin != 2)) error ("algebraic_sum requires 1 or 2 arguments\n"); elseif (!(isreal (x) && isreal (y))) error ("algebraic_sum requires real scalar or matrix arguments\n"); elseif (nargin == 2 && ... (isscalar (x) || isscalar (y) || ... isequal (size (x), size (y)))) retval = x + y - x .* y; elseif (nargin == 1 && isvector (x)) retval = algebraic_sum_of_vector (x); elseif (nargin == 1 && ndims (x) == 2) num_cols = columns (x); retval = zeros (1, num_cols); for i = 1 : num_cols retval(i) = algebraic_sum_of_vector (x(:, i)); endfor else error ("invalid arguments to function algebraic_sum\n"); endif endfunction function retval = algebraic_sum_of_vector (real_vector) x = 0; for i = 1 : length (real_vector) y = real_vector(i); x = x + y - x * y; endfor retval = x; endfunction %!test %! x = [5 2]; %! z = algebraic_sum(x); %! assert(z, -3); %!test %! x = [5 2 3 6]; %! y = [-1 0 2 3]; %! z = algebraic_sum(x, y); %! assert(z, [9 2 -1 -9]); ## Test input validation %!error %! algebraic_sum() %!error %! algebraic_sum(1, 2, 3) %!error %! algebraic_sum(2j) %!error %! algebraic_sum(1, 2j) %!error %! algebraic_sum([1 2j]) %!error %! algebraic_sum([1 2], [1 2 3]) %!error %! algebraic_sum([1 2], [1 2; 3 4]) %!error %! algebraic_sum(0:100, []) fuzzy-logic-toolkit-0.6.1/inst/bounded_difference.m000066400000000000000000000074421466512601400224240ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{retval} =} bounded_difference (@var{x}) ## @deftypefnx {Function File} {@var{retval} =} bounded_difference (@var{x}, @var{y}) ## ## Return the bounded difference of the input. ## The bounded difference of two real scalars x and y is: max (0, x + y - 1) ## ## For one vector argument, apply the bounded difference to all of the elements ## of the vector. (The bounded difference is associative.) For one ## two-dimensional matrix argument, return a vector of the bounded difference ## of each column. ## ## For two vectors or matrices of identical dimensions, or for one scalar and ## one vector or matrix argument, return the pairwise bounded difference. ## ## @seealso{algebraic_product, algebraic_sum, bounded_sum, drastic_product, drastic_sum, einstein_product, einstein_sum, hamacher_product, hamacher_sum} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy bounded_difference ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: bounded_difference.m ## Last-Modified: 26 Jul 2024 function retval = bounded_difference (x, y = 0) if ((nargin != 1) && (nargin != 2)) error ("bounded_difference requires 1 or 2 arguments\n"); elseif (!(isreal (x) && isreal (y))) error ("bounded_difference requires real scalar or matrix arguments\n"); elseif (nargin == 2 && ... (isscalar (x) || isscalar (y) || ... isequal (size (x), size (y)))) retval = max (0, (x + y - 1)); elseif (nargin == 1 && isvector (x)) retval = bounded_difference_of_vector (x); elseif (nargin == 1 && ndims (x) == 2) num_cols = columns (x); retval = zeros (1, num_cols); for i = 1 : num_cols retval(i) = bounded_difference_of_vector (x(:, i)); endfor else error ("invalid arguments to function bounded_difference\n"); endif endfunction function retval = bounded_difference_of_vector (real_vector) x = 1; for i = 1 : length (real_vector) y = real_vector(i); x = max (0, (x + y - 1)); endfor retval = x; endfunction %!test %! x = [5 2]; %! z = bounded_difference(x); %! assert(z, 6); %!test %! x = [5 2 3 -6]; %! y = [-1 0 2 3]; %! z = bounded_difference(x, y); %! assert(z, [3 1 4 0]); ## Test input validation %!error %! bounded_difference() %!error %! bounded_difference(1, 2, 3) %!error %! bounded_difference(2j) %!error %! bounded_difference(1, 2j) %!error %! bounded_difference([1 2j]) %!error %! bounded_difference([1 2], [1 2 3]) %!error %! bounded_difference([1 2], [1 2; 3 4]) %!error %! bounded_difference(0:100, []) fuzzy-logic-toolkit-0.6.1/inst/bounded_sum.m000066400000000000000000000071031466512601400211300ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{retval} =} bounded_sum (@var{x}) ## @deftypefnx {Function File} {@var{retval} =} bounded_sum (@var{x}, @var{y}) ## ## Return the bounded sum of the input. ## The bounded sum of two real scalars x and y is: min (1, x + y) ## ## For one vector argument, apply the bounded sum to all of elements of ## the vector. (The bounded sum is associative.) For one two-dimensional ## matrix argument, return a vector of the bounded sum of each column. ## ## For two vectors or matrices of identical dimensions, or for one scalar and ## one vector or matrix argument, return the pairwise bounded sum. ## ## @seealso{algebraic_product, algebraic_sum, bounded_difference, drastic_product, drastic_sum, einstein_product, einstein_sum, hamacher_product, hamacher_sum} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy bounded_sum ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: bounded_sum.m ## Last-Modified: 26 Jul 2024 function retval = bounded_sum (x, y = 0) if ((nargin != 1) && (nargin != 2)) error ("bounded_sum requires 1 or 2 arguments\n"); elseif (!(isreal (x) && isreal (y))) error ("bounded_sum requires real scalar or matrix arguments\n"); elseif (nargin == 2 && ... (isscalar (x) || isscalar (y) || ... isequal (size (x), size (y)))) retval = min (1, (x + y)); elseif (nargin == 1 && isvector (x)) retval = bounded_sum_of_vector (x); elseif (nargin == 1 && ndims (x) == 2) num_cols = columns (x); retval = zeros (1, num_cols); for i = 1 : num_cols retval(i) = bounded_sum_of_vector (x(:, i)); endfor else error ("invalid arguments to function bounded_sum\n"); endif endfunction function retval = bounded_sum_of_vector (real_vector) x = 0; for i = 1 : length (real_vector) y = real_vector(i); x = min (1, (x + y)); endfor retval = x; endfunction %!test %! x = [0.5 0.2]; %! z = bounded_sum(x); %! assert(z, 0.7, 1e-5); %!test %! x = [0.5 0.2 0.3 0.6]; %! y = [1 0 0.2 0.3]; %! z = bounded_sum(x, y); %! assert(z, [1 0.2 0.5 0.9], 1e-5); ## Test input validation %!error %! bounded_sum() %!error %! bounded_sum(1, 2, 3) %!error %! bounded_sum(2j) %!error %! bounded_sum(1, 2j) %!error %! bounded_sum([1 2j]) %!error %! bounded_sum([1 2], [1 2 3]) %!error %! bounded_sum([1 2], [1 2; 3 4]) %!error %! bounded_sum(0:100, []) fuzzy-logic-toolkit-0.6.1/inst/cubic_approx_demo.m000066400000000000000000000043361466512601400223130ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Script File} {} cubic_approx_demo ## ## Demonstrate the use of the Octave Fuzzy Logic Toolkit to approximate a ## non-linear function using a Sugeno-type FIS with linear output functions. ## ## The demo: ## @itemize @bullet ## @item ## reads an FIS structure from a file ## @item ## plots the input membership functions ## @item ## plots the (linear) output functions ## @item ## plots the FIS output as a function of the input ## @end itemize ## ## @seealso{heart_disease_demo_1, heart_disease_demo_2, investment_portfolio_demo, linear_tip_demo, mamdani_tip_demo, sugeno_tip_demo} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy tests demos ## Directory: fuzzy-logic-toolkit/inst ## Filename: cubic_approx_demo.m ## Last-Modified: 4 Jun 2024 ## Read the FIS structure from a file. fis = readfis ('cubic_approximator.fis'); ## Plot the input membership functions and linear output functions. plotmf (fis, 'input', 1); plotmf (fis, 'output', 1, -150, 150); ## Plot the FIS output y as a function of the input x. gensurf (fis); %!test %! fis = readfis ('cubic_approximator.fis'); %! cubes = evalfis([-2.5; -2; -1.5; -1; 0; 1; 1.5; 2; 2.5], fis, 101); %! expected_result = ... %! [-13.7500 %! -8.0000 %! -2.2500 %! -1.0000 %! 0 %! 1.0000 %! 2.2500 %! 8.0000 %! 13.7500]; %! assert(cubes, expected_result, 1e-4); fuzzy-logic-toolkit-0.6.1/inst/cubic_approximator.fis000066400000000000000000000045061466512601400230470ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fis ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: cubic_approximator.fis ## Last-Modified: 28 Aug 2012 [System] Name='Cubic-Approximator' Type='sugeno' Version=2.0 NumInputs=1 NumOutputs=1 NumRules=11 AndMethod='min' OrMethod='max' ImpMethod='min' AggMethod='max' DefuzzMethod='wtaver' [Input1] Name='X' Range=[-5 5] NumMFs=11 MF1 = 'About-Neg-Five':'trimf', [-6 -5 -4] MF2 = 'About-Neg-Four':'trimf', [-5 -4 -3] MF3 = 'About-Neg-Three':'trimf', [-4 -3 -2] MF4 = 'About-Neg-Two':'trimf', [-3 -2 -1] MF5 = 'About-Neg-One':'trimf', [-2 -1 0] MF6 = 'About-Zero':'trimf', [-1 0 1] MF7 = 'About-One':'trimf', [0 1 2] MF8 = 'About-Two':'trimf', [1 2 3] MF9 = 'About-Three':'trimf', [2 3 4] MF10 = 'About-Four':'trimf', [3 4 5] MF11 = 'About-Five':'trimf', [4 5 6] [Output1] Name='Approx-X-Cubed' Range=[-5 5] NumMFs=11 MF1 = 'Tangent-at-Neg-Five':'linear', [75 250] MF2 = 'Tangent-at-Neg-Four':'linear', [48 128] MF3 = 'Tangent-at-Neg-Three':'linear', [27 54] MF4 = 'Tangent-at-Neg-Two':'linear', [12 16] MF5 = 'Tangent-at-Neg-One':'linear', [3 2] MF6 = 'Tangent-at-Zero':'linear', [0 0] MF7 = 'Tangent-at-One':'linear', [3 -2] MF8 = 'Tangent-at-Two':'linear', [12 -16] MF9 = 'Tangent-at-Three':'linear', [27 -54] MF10 = 'Tangent-at-Four':'linear', [48 -128] MF11 = 'Tangent-at-Five':'linear', [75 -250] [Rules] 1, 1 (1) : 1 2, 2 (1) : 1 3, 3 (1) : 1 4, 4 (1) : 1 5, 5 (1) : 1 6, 6 (1) : 1 7, 7 (1) : 1 8, 8 (1) : 1 9, 9 (1) : 1 10, 10 (1) : 1 11, 11 (1) : 1 fuzzy-logic-toolkit-0.6.1/inst/defuzz.m000066400000000000000000000252621466512601400201410ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{crisp_x} =} defuzz (@var{x}, @var{y}, @var{defuzz_method}) ## @deftypefnx {Function File} {@var{crisp_x} =} defuzz (@var{[x1 x2 ... xn]}, @var{[y1 y2 ... yn]}, @var{defuzz_method}) ## ## For a given domain, set of fuzzy function values, and defuzzification method, ## return the defuzzified (crisp) value of the fuzzy function. ## ## The arguments @var{x} and @var{y} must be either two real numbers or ## two equal-length, non-empty vectors of reals, with the elements of @var{x} ## strictly increasing. @var{defuzz_method} must be a (case-sensitive) string ## corresponding to a defuzzification method. Defuzz handles both built-in ## and custom defuzzification methods. ## ## The built-in defuzzification methods are: ## ## @multitable @columnfractions .20 .75 ## @headitem Method @tab Value Returned ## @item centroid ## @tab Return the x-value of the centroid. ## @item bisector ## @tab Return the x-value of the vertical bisector of the area. ## @item mom ## @tab Return the mean x-value of the points with maximum y-values. ## @item som ## @tab Return the smallest (absolute) x-value of the points with ## maximum y-values. ## @item lom ## @tab Return the largest (absolute) x-value of the points with ## maximum y-values. ## @item wtaver ## @tab Return the weighted average of the x-values, with the y-values ## used as weights. ## @item wtsum ## @tab Return the weighted sum of the x-values, with the y-values ## used as weights. ## @end multitable ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy defuzzification ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: defuzz.m ## Last-Modified: 10 Jun 2024 ##---------------------------------------------------------------------- function crisp_x = defuzz (x, y, defuzz_method) ## If the caller did not supply 3 argument values with the correct ## types, print an error message and halt. if (nargin != 3) error ("defuzz requires 3 arguments\n"); elseif (!is_domain (x)) error ("defuzz's first argument must be a valid domain\n"); elseif (!(isvector (y) && isreal (y) && length (x) == length (y))) error ("defuzz's 1st and 2nd arguments must have the same length\n"); elseif (!is_string (defuzz_method)) error ("defuzz's third argument must be a string\n"); endif ## Calculate and return the defuzzified (crisp_x) value using the ## method specified by the argument defuzz_method. crisp_x = str2func (defuzz_method) (x, y); endfunction ##---------------------------------------------------------------------- ## Usage: crisp_x = centroid (x, y) ## crisp_x = centroid ([x1 x2 ... xn], [y1 y2 ... yn]) ## ## For a given domain (x or [x1 x2 ... xn]) and corresponding y-values ## (y or [y1 y2 ... yn]), return the x-value of the centroid of the ## region described by the points (xi, yi). ## ## Both arguments are assumed to be reals or non-empty vectors of reals. ## In addition, x is assumed to be strictly increasing, and x and y are ## assumed to be of equal length. ##---------------------------------------------------------------------- function crisp_x = centroid (x, y) crisp_x = trapz (x, x.*y) / trapz (x, y); endfunction ##---------------------------------------------------------------------- ## Usage: crisp_x = bisector (x, y) ## crisp_x = bisector ([x1 x2 ... xn], [y1 y2 ... yn]) ## ## For a given domain (x or [x1 x2 ... xn]) and corresponding y-values ## (y or [y1 y2 ... yn]), return the x-value of a bisector of the region ## described by the points (xi, yi). ## ## Both arguments are assumed to be reals or non-empty vectors of reals. ## In addition, x is assumed to be strictly increasing, and x and y are ## assumed to be of equal length. ##---------------------------------------------------------------------- function crisp_x = bisector (x, y) ## Find the bisector using a binary search. To ensure that the ## function terminates, add a counter to limit the iterations to the ## length of the vectors x and y. half_area = trapz (x, y) / 2; x_len = length (x); upper = x_len; lower = 1; count = 1; while ((lower <= upper) && (count++ < x_len)) midpoint = round ((lower + upper)/2); left_domain = [ones(1, midpoint), zeros(1, x_len-midpoint)]; left_y_vals = left_domain .* y; left_area = trapz (x, left_y_vals); error = left_area - half_area; if (error > 0) upper = midpoint; else lower = midpoint; endif endwhile crisp_x = midpoint; endfunction ##---------------------------------------------------------------------- ## Usage: crisp_x = mom (x, y) ## crisp_x = mom ([x1 x2 ... xn], [y1 y2 ... yn]) ## ## For a given domain (x or [x1 x2 ... xn]) and corresponding y-values ## (y or [y1 y2 ... yn]), return the "Mean of Maximum"; that is, return ## the average of the x-values corresponding to the maximum y-value ## in y. ## ## Both arguments are assumed to be reals or non-empty vectors of reals. ## In addition, x is assumed to be strictly increasing, and x and y are ## assumed to be of equal length. ##---------------------------------------------------------------------- function crisp_x = mom (x, y) max_y = max (y); #y_val = @(y_val) if (y_val == max_y) 1 else 0 endif; y_val = @(y_val) 1 * (y_val == max_y); max_y_locations = arrayfun (y_val, y); crisp_x = sum (x .* max_y_locations) / sum (max_y_locations); endfunction ##---------------------------------------------------------------------- ## Usage: crisp_x = som (x, y) ## crisp_x = som ([x1 x2 ... xn], [y1 y2 ... yn]) ## ## For a given domain (x or [x1 x2 ... xn]) and corresponding y-values ## (y or [y1 y2 ... yn]), return the "Smallest of Maximum"; that is, ## return the smallest x-value corresponding to the maximum y-value ## in y. ## ## Both arguments are assumed to be reals or non-empty vectors of reals. ## In addition, x is assumed to be strictly increasing, and x and y are ## assumed to be of equal length. ##---------------------------------------------------------------------- function crisp_x = som (x, y) max_y = max (y); #y_val = @(y_val) if (y_val == max_y) 1 else (NaN) endif; y_val = @(y_val) one_or_NaN(y_val, max_y); max_y_locations = arrayfun (y_val, y); crisp_x = min (x .* max_y_locations); endfunction ##---------------------------------------------------------------------- ## Usage: crisp_x = lom (x, y) ## crisp_x = lom ([x1 x2 ... xn], [y1 y2 ... yn]) ## ## For a given domain (x or [x1 x2 ... xn]) and corresponding y-values ## (y or [y1 y2 ... yn]), return the "Largest of Maximum"; that is, ## return the largest x-value corresponding to the maximum y-value in y. ## ## Both arguments are assumed to be reals or non-empty vectors of reals. ## In addition, x is assumed to be strictly increasing, and x and y are ## assumed to be of equal length. ##---------------------------------------------------------------------- function crisp_x = lom (x, y) max_y = max (y); #y_val = @(y_val) if (y_val == max_y) 1 else (NaN) endif; y_val = @(y_val) one_or_NaN(y_val, max_y); max_y_locations = arrayfun (y_val, y); crisp_x = max (x .* max_y_locations); endfunction ##---------------------------------------------------------------------- ## Usage: one_or_NaN (a, b) ## ## Return 1 if the arguments are equal, and otherwise return NaN. ## Called by som and lom (immediately above) to fix anonymous function ## bodies, which must be expressions, not statements. ## ## Examples: ## one_or_NaN (2, 2) ==> 1 ## one_or_NaN (2, 3) ==> NaN ##---------------------------------------------------------------------- function retval = one_or_NaN (a, b) if (a == b) retval = 1; else retval = NaN; endif endfunction ##---------------------------------------------------------------------- ## Usage: retval = wtaver (values, weights) ## ## Return the weighted average of the values. The parameters are assumed ## to be equal-length vectors of real numbers. ## ## Examples: ## wtaver ([1 2 3 4], [1 1 1 1]) ==> 2.5 ## wtaver ([1 2 3 4], [1 2 3 4]) ==> 3 ## wtaver ([1 2 3 4], [0 0 1 1]) ==> 3.5 ##---------------------------------------------------------------------- function retval = wtaver (values, weights) retval = sum (weights .* values) / sum (weights); endfunction ##---------------------------------------------------------------------- ## Usage: retval = wtsum (values, weights) ## ## Return the weighted sum of the values. The parameters are assumed to ## be equal-length vectors of real numbers. ## ## Examples: ## wtsum ([1 2 3 4], [1 1 1 1]) ==> 10 ## wtsum ([1 2 3 4], [1 2 3 4]) ==> 30 ## wtsum ([1 2 3 4], [0 0 1 1]) ==> 7 ##---------------------------------------------------------------------- function retval = wtsum (values, weights) retval = sum (weights .* values); endfunction ## Test each of the defuzzification methods %!assert(defuzz([1 2 3 4], [1 2 3 4], 'centroid'), 2.8667, 1e-4) %!assert(defuzz([1 2 3 4], [1 2 3 4], 'bisector'), 3) %!assert(defuzz([1 2 3 4], [1 2 3 4], 'mom'), 4) %!assert(defuzz([1 2 3 4], [1 2 3 4], 'som'), 4) %!assert(defuzz([1 2 3 4], [1 2 3 4], 'lom'), 4) %!assert(defuzz([1 2 3 4], [1 1 1 1], 'wtaver'), 2.5) %!assert(defuzz([1 2 3 4], [1 2 3 4], 'wtaver'), 3) %!assert(defuzz([1 2 3 4], [0 0 1 1], 'wtaver'), 3.5) %!assert(defuzz([1 2 3 4], [1 1 1 1], 'wtsum'), 10) %!assert(defuzz([1 2 3 4], [1 2 3 4], 'wtsum'), 30) %!assert(defuzz([1 2 3 4], [0 0 1 1], 'wtsum'), 7) ## Test input validation %!error %! defuzz() %!error %! defuzz(1) %!error %! defuzz(1, 2) %!error %! defuzz(1, 2, 3, 4) %!error %! defuzz([1 0], 2, 3) %!error %! defuzz([0 1], 2, 3) %!error %! defuzz([0 1], [2 3], 3) fuzzy-logic-toolkit-0.6.1/inst/drastic_product.m000066400000000000000000000101561466512601400220170ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{retval} =} drastic_product (@var{x}) ## @deftypefnx {Function File} {@var{retval} =} drastic_product (@var{x}, @var{y}) ## ## Return the drastic product of the input. ## ## The drastic product of two real scalars x and y is: ## ## @verbatim ## min (x, y) if max (x, y) == 1 ## 0 otherwise ## @end verbatim ## ## For one vector argument, apply the drastic product to all of the elements ## of the vector. (The drastic product is associative.) For one ## two-dimensional matrix argument, return a vector of the drastic product ## of each column. ## ## For two vectors or matrices of identical dimensions, or for one scalar and ## one vector or matrix argument, return the pairwise drastic product. ## ## @seealso{algebraic_product, algebraic_sum, bounded_difference, bounded_sum, drastic_sum, einstein_product, einstein_sum, hamacher_product, hamacher_sum} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy drastic_product ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: drastic_product.m ## Last-Modified: 26 Jul 2024 function retval = drastic_product (x, y = 0) if (nargin == 0 || nargin > 2 || !is_real_matrix (x) || !is_real_matrix (y)) error ("invalid arguments to function drastic_product\n"); elseif (nargin == 1) if (isvector (x)) retval = vector_arg (x); elseif (ndims (x) == 2) retval = matrix_arg (x); else error ("invalid arguments to function drastic_product\n"); endif elseif (nargin == 2) if (isequal (size (x), size (y))) retval = arrayfun (@scalar_args, x, y); elseif (isscalar (x) && ismatrix (y)) x = x * ones (size (y)); retval = arrayfun (@scalar_args, x, y); elseif (ismatrix (x) && isscalar (y)) y = y * ones (size (x)); retval = arrayfun (@scalar_args, x, y); else error ("invalid arguments to function drastic_product\n"); endif endif endfunction function retval = scalar_args (x, y) if (max (x, y) == 1) retval = min (x, y); else retval = 0; endif endfunction function retval = vector_arg (x) if (isempty (x)) retval = 1; elseif (max (x) == 1) retval = min (x); else retval = 0; endif endfunction function retval = matrix_arg (x) num_cols = columns (x); retval = zeros (1, num_cols); for i = 1 : num_cols retval(i) = vector_arg (x(:, i)); endfor endfunction %!test %! x = [0.5 0.2]; %! z = drastic_product(x); %! assert(z, 0); %!test %! x = [0.5 0.2 0.3 1]; %! y = [1 0 0.2 0.3]; %! z = drastic_product(x, y); %! assert(z, [0.5 0 0 0.3]); ## Test input validation %!error %! drastic_product() %!error %! drastic_product(1, 2, 3) %!error %! drastic_product(2j) %!error %! drastic_product(1, 2j) %!error %! drastic_product([1 2j]) %!error %! drastic_product([1 2], [1 2 3]) %!error %! drastic_product([1 2], [1 2; 3 4]) %!error %! drastic_product(0:100, []) fuzzy-logic-toolkit-0.6.1/inst/drastic_sum.m000066400000000000000000000077611466512601400211530ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{retval} =} drastic_sum (@var{x}) ## @deftypefnx {Function File} {@var{retval} =} drastic_sum (@var{x}, @var{y}) ## ## Return the drastic sum of the input. ## ## The drastic sum of two real scalars x and y is: ## ## @verbatim ## max (x, y) if min (x, y) == 0 ## 1 otherwise ## @end verbatim ## ## For one vector argument, apply the drastic sum to all of the elements ## of the vector. (The drastic sum is associative.) For one ## two-dimensional matrix argument, return a vector of the drastic sum ## of each column. ## ## For two vectors or matrices of identical dimensions, or for one scalar and ## one vector or matrix argument, return the pairwise drastic sum. ## ## @seealso{algebraic_product, algebraic_sum, bounded_difference, bounded_sum, drastic_product, einstein_product, einstein_sum, hamacher_product, hamacher_sum} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy drastic_sum ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: drastic_sum.m ## Last-Modified: 26 Jul 2024 function retval = drastic_sum (x, y = 0) if (nargin == 0 || nargin > 2 || !is_real_matrix (x) || !is_real_matrix (y)) error ("invalid arguments to function drastic_sum\n"); elseif (nargin == 1) if (isvector (x)) retval = vector_arg (x); elseif (ndims (x) == 2) retval = matrix_arg (x); else error ("invalid arguments to function drastic_sum\n"); endif elseif (nargin == 2) if (isequal (size (x), size (y))) retval = arrayfun (@scalar_args, x, y); elseif (isscalar (x) && ismatrix (y)) x = x * ones (size (y)); retval = arrayfun (@scalar_args, x, y); elseif (ismatrix (x) && isscalar (y)) y = y * ones (size (x)); retval = arrayfun (@scalar_args, x, y); else error ("invalid arguments to function drastic_sum\n"); endif endif endfunction function retval = scalar_args (x, y) if (min (x, y) == 0) retval = max (x, y); else retval = 1; endif endfunction function retval = vector_arg (x) if (isempty (x)) retval = 0; elseif (min (x) == 0) retval = max (x); else retval = 1; endif endfunction function retval = matrix_arg (x) num_cols = columns (x); retval = zeros (1, num_cols); for i = 1 : num_cols retval(i) = vector_arg (x(:, i)); endfor endfunction %!test %! x = [0.5 0.2]; %! z = drastic_sum(x); %! assert(z, 1); %!test %! x = [0.5 0.2 0.3 1]; %! y = [1 0 0.2 0.3]; %! z = drastic_sum(x, y); %! assert(z, [1 0.2 1 1]); ## Test input validation %!error %! drastic_sum() %!error %! drastic_sum(1, 2, 3) %!error %! drastic_sum(2j) %!error %! drastic_sum(1, 2j) %!error %! drastic_sum([1 2j]) %!error %! drastic_sum([1 2], [1 2 3]) %!error %! drastic_sum([1 2], [1 2; 3 4]) %!error %! drastic_sum(0:100, []) fuzzy-logic-toolkit-0.6.1/inst/dsigmf.m000066400000000000000000000116321466512601400200770ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} dsigmf (@var{x}, @var{params}) ## @deftypefnx {Function File} {@var{y} =} dsigmf (@var{[x1 x2 ... xn]}, @var{[a1 c1 a2 c2]}) ## ## For a given domain @var{x} and parameters @var{params} (or ## @var{[a1 c1 a2 c2]}), return the corresponding @var{y} values for the ## difference between two sigmoidal membership functions. ## ## The argument @var{x} must be a real number or a non-empty list of strictly ## increasing real numbers, and @var{a1}, @var{c1}, @var{a2}, and @var{c2} must ## be real numbers. This membership function satisfies the equation: ## ## @verbatim ## f(x) = 1/(1 + exp(-a1*(x - c1))) - 1/(1 + exp(-a2*(x - c2))) ## @end verbatim ## ## and in addition, is bounded above and below by 1 and 0 (regardless of the ## value given by the formula above). ## ## If the parameters @var{a1} and @var{a2} are positive and @var{c1} and ## @var{c2} are far enough apart with @var{c1} < @var{c2}, then: ## ## @verbatim ## (a1)/4 ~ the rising slope at c1 ## c1 ~ the left inflection point ## (-a2)/4 ~ the falling slope at c2 ## c2 ~ the right inflection point ## @end verbatim ## ## and at each inflection point, the value of the function is about 0.5: ## ## @verbatim ## f(c1) ~ f(c2) ~ 0.5. ## @end verbatim ## ## Here, the symbol ~ means "approximately equal". ## ## To run the demonstration code, type "@t{demo dsigmf}" (without the quotation ## marks) at the Octave prompt. ## ## @seealso{gauss2mf, gaussmf, gbellmf, pimf, psigmf, sigmf, smf, trapmf, trimf, zmf} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy membership sigmoidal ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: dsigmf.m ## Last-Modified: 26 Jul 2024 function y = dsigmf (x, params) ## If the caller did not supply 2 argument values with the correct ## types, print an error message and halt. if (nargin != 2) error ("dsigmf requires 2 arguments\n"); elseif (!is_domain (x)) error ("dsigmf's first argument must be a valid domain\n"); elseif (!are_mf_params ('dsigmf', params)) error ("dsigmf's second argument must be a parameter vector\n"); endif ## Calculate and return the y values of the membership function on the ## domain x. a1 = params(1); c1 = params(2); a2 = params(3); c2 = params(4); y_val = @(x_val) max (0, ... min (1, 1 / (1 + exp (-a1 * (x_val - c1))) - ... 1 / (1 + exp (-a2 * (x_val - c2))))); y = arrayfun (y_val, x); endfunction %!demo %! x = 0:100; %! params = [0.5 20 0.3 60]; %! y1 = dsigmf(x, params); %! params = [0.3 20 0.2 60]; %! y2 = dsigmf(x, params); %! params = [0.2 20 0.1 60]; %! y3 = dsigmf(x, params); %! figure('NumberTitle', 'off', 'Name', 'dsigmf demo'); %! plot(x, y1, 'r;params = [0.5 20 0.3 60];', 'LineWidth', 2) %! hold on; %! plot(x, y2, 'b;params = [0.3 20 0.2 60];', 'LineWidth', 2) %! hold on; %! plot(x, y3, 'g;params = [0.2 20 0.1 60];', 'LineWidth', 2) %! ylim([-0.1 1.1]); %! xlabel('Crisp Input Value', 'FontWeight', 'bold'); %! ylabel('Degree of Membership', 'FontWeight', 'bold'); %! grid; %!test %! x = 0:10; %! params = [5 2 3 6]; %! y = [4.5383e-05 6.6925e-03 0.5000 0.9932 0.9975 0.9526 ... %! 0.5000 0.047426 2.4726e-03 1.2339e-04 6.1442e-06]; %! z = dsigmf(x, params); %! assert(z, y, 1e-4); ## Test input validation %!error %! dsigmf() %!error %! dsigmf(1) %!error %! dsigmf([1 0], 2) %!error %! dsigmf(1, 2) %!error %! dsigmf(1, 2, 3) %!error %! dsigmf(0:100, []) %!error %! dsigmf(0:100, [30]) %!error %! dsigmf(0:100, [2 3]) %!error %! dsigmf(0:100, [90 80 30]) %!error %! dsigmf(0:100, 'abc') fuzzy-logic-toolkit-0.6.1/inst/einstein_product.m000066400000000000000000000101221466512601400221750ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{retval} =} einstein_product (@var{x}) ## @deftypefnx {Function File} {@var{retval} =} einstein_product (@var{x}, @var{y}) ## ## Return the Einstein product of the input. ## The Einstein product of two real scalars x and y is: ## (x * y) / (2 - (x + y - x * y)) ## ## For one vector argument, apply the Einstein product to all of the elements ## of the vector. (The Einstein product is associative.) For one ## two-dimensional matrix argument, return a vector of the Einstein product ## of each column. ## ## For two vectors or matrices of identical dimensions, or for one scalar and ## one vector or matrix argument, return the pairwise Einstein product. ## ## @seealso{algebraic_product, algebraic_sum, bounded_difference, bounded_sum, drastic_product, drastic_sum, einstein_sum, hamacher_product, hamacher_sum} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy einstein_product ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: einstein_product.m ## Last-Modified: 26 Jul 2024 function retval = einstein_product (x, y = 0) if (nargin == 0 || nargin > 2 || !is_real_matrix (x) || !is_real_matrix (y)) error ("invalid arguments to function einstein_product\n"); elseif (nargin == 1) if (isvector (x)) retval = vector_arg (x); elseif (ndims (x) == 2) retval = matrix_arg (x); else error ("invalid arguments to function einstein_product\n"); endif elseif (nargin == 2) if (isequal (size (x), size (y))) retval = arrayfun (@scalar_args, x, y); elseif (isscalar (x) && ismatrix (y)) x = x * ones (size (y)); retval = arrayfun (@scalar_args, x, y); elseif (ismatrix (x) && isscalar (y)) y = y * ones (size (x)); retval = arrayfun (@scalar_args, x, y); else error ("invalid arguments to function einstein_product\n"); endif endif endfunction function retval = scalar_args (x, y) retval = (x * y) / (2 - (x + y - x * y)); endfunction function retval = vector_arg (real_vector) x = 1; for i = 1 : length (real_vector) y = real_vector(i); x = (x * y) / (2 - (x + y - x * y)); endfor retval = x; endfunction function retval = matrix_arg (x) num_cols = columns (x); retval = zeros (1, num_cols); for i = 1 : num_cols retval(i) = vector_arg (x(:, i)); endfor endfunction %!test %! x = [5 3]; %! z = einstein_product(x); %! assert(z, 1.6667, 1e-3); %!test %! x = [5 2 3 6]; %! y = [-1 1 2 3]; %! z = einstein_product(x, y); %! assert(z, [0.7134 2.0000 2.0000 1.6364], 1e-3); ## Test input validation %!error %! einstein_product() %!error %! einstein_product(2j) %!error %! einstein_product(1, 2j) %!error %! einstein_product([1 2j]) %!error %! einstein_product(1, 2, 3) %!error %! einstein_product([1 2], [1 2 3]) %!error %! einstein_product([1 2], [1 2; 3 4]) %!error %! einstein_product(0:100, []) fuzzy-logic-toolkit-0.6.1/inst/einstein_sum.m000066400000000000000000000076561466512601400213430ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{retval} =} einstein_sum (@var{x}) ## @deftypefnx {Function File} {@var{retval} =} einstein_sum (@var{x}, @var{y}) ## ## Return the Einstein sum of the input. ## The Einstein sum of two real scalars x and y is: (x + y) / (1 + x * y) ## ## For one vector argument, apply the Einstein sum to all of the elements ## of the vector. (The Einstein sum is associative.) For one ## two-dimensional matrix argument, return a vector of the Einstein sum ## of each column. ## ## For two vectors or matrices of identical dimensions, or for one scalar and ## one vector or matrix argument, return the pairwise Einstein sum. ## ## @seealso{algebraic_product, algebraic_sum, bounded_difference, bounded_sum, drastic_product, drastic_sum, einstein_product, hamacher_product, hamacher_sum} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy einstein_sum ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: einstein_sum.m ## Last-Modified: 26 Jul 2024 function retval = einstein_sum (x, y = 0) if (nargin == 0 || nargin > 2 || !is_real_matrix (x) || !is_real_matrix (y)) error ("invalid arguments to function einstein_sum\n"); elseif (nargin == 1) if (isvector (x)) retval = vector_arg (x); elseif (ndims (x) == 2) retval = matrix_arg (x); else error ("invalid arguments to function einstein_sum\n"); endif elseif (nargin == 2) if (isequal (size (x), size (y))) retval = arrayfun (@scalar_args, x, y); elseif (isscalar (x) && ismatrix (y)) x = x * ones (size (y)); retval = arrayfun (@scalar_args, x, y); elseif (ismatrix (x) && isscalar (y)) y = y * ones (size (x)); retval = arrayfun (@scalar_args, x, y); else error ("invalid arguments to function einstein_sum\n"); endif endif endfunction function retval = scalar_args (x, y) retval = (x + y) / (1 + x * y); endfunction function retval = vector_arg (real_vector) x = 0; for i = 1 : length (real_vector) y = real_vector(i); x = (x + y) / (1 + x * y); endfor retval = x; endfunction function retval = matrix_arg (x) num_cols = columns (x); retval = zeros (1, num_cols); for i = 1 : num_cols retval(i) = vector_arg (x(:, i)); endfor endfunction %!test %! x = [5 3]; %! z = einstein_sum(x); %! assert(z, 0.5000); %!test %! x = [5 2 3 6]; %! y = [-1 1 2 3]; %! z = einstein_sum(x, y); %! assert(z, [-1.000 1.000 0.7143 0.4737], 1e-4); ## Test input validation %!error %! einstein_sum() %!error %! einstein_sum(2j) %!error %! einstein_sum(1, 2j) %!error %! einstein_sum([1 2j]) %!error %! einstein_sum(1, 2, 3) %!error %! einstein_sum([1 2], [1 2 3]) %!error %! einstein_sum([1 2], [1 2; 3 4]) %!error %! einstein_sum(0:100, []) fuzzy-logic-toolkit-0.6.1/inst/evalfis.m000066400000000000000000000260401466512601400202560ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{output} =} evalfis (@var{user_input}, @var{fis}) ## @deftypefnx {Function File} {@var{output} =} evalfis (@var{user_input}, @var{fis}, @var{num_points}) ## @deftypefnx {Function File} {[@var{output}, @var{rule_input}, @var{rule_output}, @var{fuzzy_output}] =} evalfis (@var{user_input}, @var{fis}) ## @deftypefnx {Function File} {[@var{output}, @var{rule_input}, @var{rule_output}, @var{fuzzy_output}] =} evalfis (@var{user_input}, @var{fis}, @var{num_points}) ## ## Return the crisp output(s) of an FIS for each row in a matrix of crisp input ## values. ## Also, for the last row of @var{user_input}, return the intermediate results: ## ## @multitable @columnfractions .25 .65 ## @headitem Intermediate Result @tab Value Returned ## @item @var{rule_input} ## @tab a matrix of the degree to which each FIS rule matches each ## FIS input variable ## @item @var{rule_output} ## @tab a matrix of the fuzzy output for each (rule, FIS output) pair ## @item @var{fuzzy_output} ## @tab a matrix of the aggregated output for each FIS output variable ## @end multitable ## @sp 1 ## The optional argument @var{num_points} specifies the number of points over ## which to evaluate the fuzzy values. The default value of @var{num_points} is ## 101. ## ## @strong{Argument @var{user_input}:} ## @var{user_input} is a matrix of crisp input values. Each row ## represents one set of crisp FIS input values. For an FIS that has N inputs, ## an input matrix of z sets of input values will have the form: ## ## @verbatim ## [[input_11 input_12 ... input_1N] <-- 1st row is 1st set of inputs ## [input_21 input_22 ... input_2N] <-- 2nd row is 2nd set of inputs ## [ ... ] ... ## [input_z1 input_z2 ... input_zN]] <-- zth row is zth set of inputs ## @end verbatim ## ## @strong{Return value @var{output}:} ## @var{output} is a matrix of crisp output values. Each row represents ## the set of crisp FIS output values for the corresponding row of ## @var{user_input}. For an FIS that has M outputs, an @var{output} matrix ## corresponding to the preceding input matrix will have the form: ## ## @verbatim ## [[output_11 output_12 ... output_1M] <-- 1st row is 1st set of outputs ## [output_21 output_22 ... output_2M] <-- 2nd row is 2nd set of outputs ## [ ... ] ... ## [output_z1 output_z2 ... output_zM]] <-- zth row is zth set of outputs ## @end verbatim ## ## @strong{The intermediate result @var{rule_input}:} ## The matching degree for each (rule, input value) pair is specified by the ## @var{rule_input} matrix. For an FIS that has Q rules and N input variables, ## the matrix will have the form: ## @verbatim ## in_1 in_2 ... in_N ## rule_1 [[mu_11 mu_12 ... mu_1N] ## rule_2 [mu_21 mu_22 ... mu_2N] ## [ ... ] ## rule_Q [mu_Q1 mu_Q2 ... mu_QN]] ## @end verbatim ## ## @strong{Evaluation of hedges and "not":} ## Each element of each FIS rule antecedent and consequent indicates the ## corresponding membership function, hedge, and whether or not "not" should ## be applied to the result. The index of the membership function to be used is ## given by the positive whole number portion of the antecedent/consequent ## vector entry, the hedge is given by the fractional portion (if any), and ## "not" is indicated by a minus sign. A "0" as the integer portion in any ## position in the rule indicates that the corresponding FIS input or output ## variable is omitted from the rule. ## ## For custom hedges and the four built-in hedges "somewhat," "very," ## "extremely," and "very very," the membership function value (without the ## hedge or "not") is raised to the power corresponding to the hedge. All ## hedges are rounded to 2 digits. ## ## For example, if "mu(x)" denotes the matching degree of the input to the ## corresponding membership function without a hedge or "not," then the final ## matching degree recorded in @var{rule_input} will be computed by applying ## the hedge and "not" in two steps. First, the hedge is applied: ## ## @verbatim ## (fraction == .05) <=> somewhat x <=> mu(x)^0.5 <=> sqrt(mu(x)) ## (fraction == .20) <=> very x <=> mu(x)^2 <=> sqr(mu(x)) ## (fraction == .30) <=> extremely x <=> mu(x)^3 <=> cube(mu(x)) ## (fraction == .40) <=> very very x <=> mu(x)^4 ## (fraction == .dd) <=> x <=> mu(x)^(dd/10) ## @end verbatim ## ## After applying the appropriate hedge, "not" is calculated by: ## ## @verbatim ## minus sign present <=> not x <=> 1 - mu(x) ## minus sign and hedge present <=> not x <=> 1 - mu(x)^(dd/10) ## @end verbatim ## ## Hedges and "not" in the consequent are handled similarly. ## ## @strong{The intermediate result @var{rule_output}:} ## For either a Mamdani-type FIS (that is, an FIS that does not have constant or ## linear output membership functions) or a Sugeno-type FIS (that is, an FIS ## that has only constant and linear output membership functions), ## @var{rule_output} specifies the fuzzy output for each (rule, FIS output) pair. ## The format of rule_output depends on the FIS type. ## ## For a Mamdani-type FIS, @var{rule_output} is a @var{num_points} x (Q * M) ## matrix, where Q is the number of rules and M is the number of FIS output ## variables. Each column of this matrix gives the y-values of the fuzzy ## output for a single (rule, FIS output) pair. ## ## @verbatim ## Q cols Q cols Q cols ## --------------- --------------- --------------- ## out_1 ... out_1 out_2 ... out_2 ... out_M ... out_M ## 1 [[ ] ## 2 [ ] ## ... [ ] ## num_points [ ]] ## @end verbatim ## ## For a Sugeno-type FIS, @var{rule_output} is a 2 x (Q * M) matrix. ## Each column of this matrix gives the (location, height) pair of the ## singleton output for a single (rule, FIS output) pair. ## ## @verbatim ## Q cols Q cols Q cols ## --------------- --------------- --------------- ## out_1 ... out_1 out_2 ... out_2 ... out_M ... out_M ## location [[ ] ## height [ ]] ## @end verbatim ## ## @strong{The intermediate result @var{fuzzy_output}:} ## The format of @var{fuzzy_output} depends on the FIS type ('mamdani' or ## 'sugeno'). ## ## For either a Mamdani-type FIS or a Sugeno-type FIS, @var{fuzzy_output} ## specifies the aggregated fuzzy output for each FIS output. ## ## For a Mamdani-type FIS, the aggregated @var{fuzzy_output} is a ## @var{num_points} x M matrix. Each column of this matrix gives the y-values ## of the fuzzy output for a single FIS output, aggregated over all rules. ## ## @verbatim ## out_1 out_2 ... out_M ## 1 [[ ] ## 2 [ ] ## ... [ ] ## num_points [ ]] ## @end verbatim ## ## For a Sugeno-type FIS, the aggregated output for each FIS output is a 2 x L ## matrix, where L is the number of distinct singleton locations in the ## @var{rule_output} for that FIS output: ## ## @verbatim ## singleton_1 singleton_2 ... singleton_L ## location [[ ] ## height [ ]] ## @end verbatim ## ## Then @var{fuzzy_output} is a vector of M structures, each of which has an index and ## one of these matrices. ## ## @strong{Examples:} ## Five examples of using evalfis are shown in: ## @itemize @bullet ## @item ## heart_disease_demo_2.m ## @item ## investment_portfolio_demo.m ## @item ## linear_tip_demo.m ## @item ## mamdani_tip_demo.m ## @item ## sugeno_tip_demo.m ## @end itemize ## ## @seealso{cubic_approx_demo, heart_disease_demo_1, heart_disease_demo_2, investment_portfolio_demo, linear_tip_demo, mamdani_tip_demo, sugeno_tip_demo} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: evalfis.m ## Last-Modified: 13 Jun 2024 function [output, rule_input, rule_output, fuzzy_output] = ... evalfis (user_input, fis, num_points = 101) ## If evalfis was called with an incorrect number of arguments, or ## the arguments do not have the correct type, print an error message ## and halt. if ((nargin != 2) && (nargin != 3)) error ("evalfis requires 2 or 3 arguments\n"); elseif (!is_fis (fis)) error ("evalfis's second argument must be an FIS structure\n"); elseif (!is_input_matrix (user_input, fis)) error ("evalfis's 1st argument must be a matrix of input values\n"); elseif (!is_pos_int (num_points)) error ("evalfis's third argument must be a positive integer\n"); endif ## Call a private function to compute the output. ## (The private function is also called by gensurf.) [output, rule_input, rule_output, fuzzy_output] = ... evalfis_private (user_input, fis, num_points); endfunction %!shared fis, food_service %! fis = readfis ('sugeno_tip_calculator.fis'); %! food_service = [1 1; 5 5; 10 10; 4 6; 6 4; 7 4]; %!test %! tip = evalfis (food_service, fis, 1001); %! expected_result = ... %! [10.000 10.000 12.500 %! 10.868 13.681 19.138 %! 17.500 17.500 20.000 %! 10.604 14.208 19.452 %! 10.427 13.687 19.033 %! 10.471 14.358 19.353]; %! assert(tip, expected_result, 1e-3); ## Test input validation %!error %! evalfis() %!error %! evalfis(1) %!error %! evalfis(1, 2, 3, 4) %!error %! evalfis(food_service, 2, 3) %!error %! evalfis(0, fis, 3) %!error %! evalfis(food_service, fis, -3) fuzzy-logic-toolkit-0.6.1/inst/evalmf.m000066400000000000000000000116561466512601400201060ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} evalmf (@var{x}, @var{param}, @var{mf_type}) ## @deftypefnx {Function File} {@var{y} =} evalmf (@var{x}, @var{param}, @var{mf_type}, @var{hedge}) ## @deftypefnx {Function File} {@var{y} =} evalmf (@var{x}, @var{param}, @var{mf_type}, @var{hedge}, @var{not_flag}) ## @deftypefnx {Function File} {@var{y} =} evalmf (@var{[x1 x2 ... xn]}, @var{[param1 ... ]}, @var{mf_type}) ## @deftypefnx {Function File} {@var{y} =} evalmf (@var{[x1 x2 ... xn]}, @var{[param1 ... ]}, @var{mf_type}, @var{hedge}) ## @deftypefnx {Function File} {@var{y} =} evalmf (@var{[x1 x2 ... xn]}, @var{[param1 ... ]}, @var{mf_type}, @var{hedge}, @var{not_flag}) ## ## For a given domain, set of parameters, membership function type, and ## optional hedge and not_flag, return the corresponding y-values for the ## membership function. ## ## The argument @var{x} must be a real number or a non-empty list of strictly ## increasing real numbers, @var{param} must be a valid parameter or a vector ## of valid parameters for @var{mf_type}, and @var{mf_type} must be a string ## corresponding to a membership function type. Evalmf handles both built-in and ## custom membership functions. ## ## For custom hedges and the four built-in hedges "somewhat", "very", ## "extremely", and "very very", raise the membership function values to ## the power corresponding to the hedge. ## ## @verbatim ## (fraction == .05) <=> somewhat x <=> mu(x)^0.5 <=> sqrt(mu(x)) ## (fraction == .20) <=> very x <=> mu(x)^2 <=> sqr(mu(x)) ## (fraction == .30) <=> extremely x <=> mu(x)^3 <=> cube(mu(x)) ## (fraction == .40) <=> very very x <=> mu(x)^4 ## (fraction == .dd) <=> x <=> mu(x)^(dd/10) ## @end verbatim ## ## The @var{not_flag} negates the membership function using: ## ## @verbatim ## mu(not(x)) = 1 - mu(x) ## @end verbatim ## ## To run the demonstration code, type "@t{demo evalmf}" (without the quotation ## marks) at the Octave prompt. ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy membership evaluate ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: evalmf.m ## Last-Modified: 12 Jun 2024 function y = evalmf (x, params, mf_type, hedge = 0, not_flag = false) ## If the caller did not supply 3 - 5 argument values with the correct ## types, print an error message and halt. if ((nargin < 3) || (nargin > 5)) error ("evalmf requires between 3 and 5 arguments\n"); elseif (!is_domain (x)) error ("evalmf's first argument must be a valid domain\n"); elseif (!is_string (mf_type)) error ("evalmf's third argument must be a string\n"); elseif (!is_real (hedge)) error ("evalmf's fourth argument must be a real number\n"); elseif (!isbool (not_flag)) error ("evalmf's fifth argument must be a Boolean\n"); endif ## Calculate and return the y values of the membership function on ## the domain x. y = evalmf_private (x, params, mf_type, hedge, not_flag); endfunction %!demo %! x = 0:100; %! params = [25 50 75]; %! mf_type = 'trimf'; %! y = evalmf(x, params, mf_type); %! figure('NumberTitle', 'off', 'Name', "evalmf(0:100, [25 50 75], 'trimf')"); %! plot(x, y, 'LineWidth', 2) %! ylim([-0.1 1.1]); %! xlabel('Crisp Input Value', 'FontWeight', 'bold'); %! ylabel('Degree of Membership', 'FontWeight', 'bold'); %! grid; %!test %! x = 0:10:100; %! params = [25 50 75]; %! mf_type = 'trimf'; %! y = evalmf(x, params, mf_type); %! assert(y, [0 0 0 0.2 0.6 1 0.6 0.2 0 0 0]); ## Test input validation %!error %! evalmf() %!error %! evalmf(1) %!error %! evalmf(1, 2) %!error %! evalmf(1, 2, 3, 4, 5, 6) %!error %! evalmf([1 0], 2, 3) %!error %! evalmf([0 1], 2, 3) %!error %! evalmf([0 1], 2, 'trimf', 2j) %!error %! evalmf([0 1], 2, 'trimf', 2, 2) fuzzy-logic-toolkit-0.6.1/inst/fcm.m000066400000000000000000000342531466512601400173770ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{cluster_centers} =} fcm (@var{input_data}, @var{num_clusters}) ## @deftypefnx {Function File} {@var{cluster_centers} =} fcm (@var{input_data}, @var{num_clusters}, @var{options}) ## @deftypefnx {Function File} {@var{cluster_centers} =} fcm (@var{input_data}, @var{num_clusters}, [@var{m}, @var{max_iterations}, @var{epsilon}, @var{display_intermediate_results}]) ## @deftypefnx {Function File} {[@var{cluster_centers}, @var{soft_partition}, @var{obj_fcn_history}] =} fcm (@var{input_data}, @var{num_clusters}) ## @deftypefnx {Function File} {[@var{cluster_centers}, @var{soft_partition}, @var{obj_fcn_history}] =} fcm (@var{input_data}, @var{num_clusters}, @var{options}) ## @deftypefnx {Function File} {[@var{cluster_centers}, @var{soft_partition}, @var{obj_fcn_history}] =} fcm (@var{input_data}, @var{num_clusters}, [@var{m}, @var{max_iterations}, @var{epsilon}, @var{display_intermediate_results}]) ## ## Using the Fuzzy C-Means algorithm, calculate and return the soft partition ## of a set of unlabeled data points. ## ## Also, if @var{display_intermediate_results} is true, display intermediate ## results after each iteration. Note that because the initial cluster ## prototypes are randomly selected locations in the ranges determined by the ## input data, the results of this function are nondeterministic. ## ## The required arguments to fcm are: ## @itemize @w ## @item ## @var{input_data}: a matrix of input data points; each row corresponds to one point ## @item ## @var{num_clusters}: the number of clusters to form ## @end itemize ## ## The optional arguments to fcm are: ## @itemize @w ## @item ## @var{m}: the parameter (exponent) in the objective function; default = 2.0 ## @item ## @var{max_iterations}: the maximum number of iterations before stopping; default = 100 ## @item ## @var{epsilon}: the stopping criteria; default = 1e-5 ## @item ## @var{display_intermediate_results}: if 1, display results after each iteration, and if 0, do not; default = 1 ## @end itemize ## ## The default values are used if any of the optional arguments are missing or ## evaluate to NaN. ## ## The return values are: ## @itemize @w ## @item ## @var{cluster_centers}: a matrix of the cluster centers; each row corresponds to one point ## @item ## @var{soft_partition}: a constrained soft partition matrix ## @item ## @var{obj_fcn_history}: the values of the objective function after each iteration ## @end itemize ## ## Three important matrices used in the calculation are X (the input points ## to be clustered), V (the cluster centers), and Mu (the membership of each ## data point in each cluster). Each row of X and V denotes a single point, ## and Mu(i, j) denotes the membership degree of input point X(j, :) in the ## cluster having center V(i, :). ## ## X is identical to the required argument @var{input_data}; V is identical ## to the output @var{cluster_centers}; and Mu is identical to the output ## @var{soft_partition}. ## ## If n denotes the number of input points and k denotes the number of ## clusters to be formed, then X, V, and Mu have the dimensions: ## ## @verbatim ## 1 2 ... #features ## 1 [[ ] ## X = input_data = 2 [ ] ## ... [ ] ## n [ ]] ## ## 1 2 ... #features ## 1 [[ ] ## V = cluster_centers = 2 [ ] ## ... [ ] ## k [ ]] ## ## 1 2 ... n ## 1 [[ ] ## Mu = soft_partition = 2 [ ] ## ... [ ] ## k [ ]] ## @end verbatim ## ## @seealso{gustafson_kessel, partition_coeff, partition_entropy, xie_beni_index} ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy partition clustering ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: fcm.m ## Last-Modified: 13 Jun 2024 function [cluster_centers, soft_partition, obj_fcn_history] = ... fcm (input_data, num_clusters, options = [2.0, 100, 1e-5, 1]) ## If fcm was called with an incorrect number of arguments, or the ## arguments do not have the correct type, print an error message ## and halt. if ((nargin != 2) && (nargin != 3)) error ("fcm requires 2 or 3 arguments\n"); elseif (!is_real_matrix (input_data)) error ("fcm's first argument must be matrix of real numbers\n"); elseif (!(is_int (num_clusters) && (num_clusters > 1))) error ("fcm's second argument must be an integer greater than 1\n"); elseif (!(isreal (options) && isvector (options))) error ("fcm's third argument must be a vector of real numbers\n"); endif ## Assign options to the more readable variable names: m, ## max_iterations, epsilon, and display_intermediate_results. ## If options are missing or NaN (not a number), use the default ## values. default_options = [2.0, 100, 1e-5, 1]; for i = 1 : 4 if ((length (options) < i) || ... isna (options(i)) || isnan (options(i))) options(i) = default_options(i); endif endfor m = options(1); max_iterations = options(2); epsilon = options(3); display_intermediate_results = options(4); ## Call a private function to compute the output. [cluster_centers, soft_partition, obj_fcn_history] = ... fcm_private (input_data, num_clusters, m, max_iterations, epsilon, display_intermediate_results); endfunction ##---------------------------------------------------------------------- ## Note: This function (fcm_private) is an implementation of Figure 13.4 ## in Fuzzy Logic: Intelligence, Control and Information, by ## J. Yen and R. Langari, Prentice Hall, 1999, page 380 ## (International Edition) and Algorithm 4.1 in Fuzzy and Neural ## Control, by Robert Babuska, November 2009, p. 63. ##---------------------------------------------------------------------- function [V, Mu, obj_fcn_history] = ... fcm_private (X, k, m, max_iterations, epsilon, ... display_intermediate_results) ## Initialize the prototypes and the calculation. V = init_cluster_prototypes (X, k); obj_fcn_history = zeros (max_iterations); convergence_criterion = epsilon + 1; iteration = 0; ## Calculate a few numbers here to reduce redundant computation. k = rows (V); n = rows (X); sqr_dist = square_distance_matrix (X, V); ## Loop until the objective function is within tolerance or the ## maximum number of iterations has been reached. while (convergence_criterion > epsilon && ... ++iteration <= max_iterations) V_previous = V; Mu = update_cluster_membership (V, X, m, k, n, sqr_dist); Mu_m = Mu .^ m; V = update_cluster_prototypes (Mu_m, X, k); sqr_dist = square_distance_matrix (X, V); obj_fcn_history(iteration) = ... compute_cluster_obj_fcn (Mu_m, sqr_dist); if (display_intermediate_results) printf ("Iteration count = %d, Objective fcn = %8.6f\n", ... iteration, obj_fcn_history(iteration)); endif convergence_criterion = ... compute_cluster_convergence (V, V_previous); endwhile ## Remove extraneous entries from the tail of the objective ## function history. if (convergence_criterion <= epsilon) obj_fcn_history = obj_fcn_history(1 : iteration); endif endfunction ##---------------------------------------------------------------------- ## FCM Demo #1 ##---------------------------------------------------------------------- %!demo %! ## This demo: %! ## - classifies a small set of unlabeled data points using %! ## the Fuzzy C-Means algorithm into two fuzzy clusters %! ## - plots the input points together with the cluster centers %! ## - evaluates the quality of the resulting clusters using %! ## three validity measures: the partition coefficient, the %! ## partition entropy, and the Xie-Beni validity index %! ## %! ## Note: The input_data is taken from Chapter 13, Example 17 in %! ## Fuzzy Logic: Intelligence, Control and Information, by %! ## J. Yen and R. Langari, Prentice Hall, 1999, page 381 %! ## (International Edition). %! %! ## Use fcm to classify the input_data. %! input_data = [2 12; 4 9; 7 13; 11 5; 12 7; 14 4]; %! number_of_clusters = 2; %! [cluster_centers, soft_partition, obj_fcn_history] = ... %! fcm (input_data, number_of_clusters) %! %! ## Plot the data points as small blue x's. %! figure ('NumberTitle', 'off', 'Name', 'FCM Demo 1'); %! for i = 1 : rows (input_data) %! plot (input_data(i, 1), input_data(i, 2), 'LineWidth', 2, ... %! 'marker', 'x', 'color', 'b'); %! hold on; %! endfor %! %! ## Plot the cluster centers as larger red *'s. %! for i = 1 : number_of_clusters %! plot (cluster_centers(i, 1), cluster_centers(i, 2), ... %! 'LineWidth', 4, 'marker', '*', 'color', 'r'); %! hold on; %! endfor %! %! ## Make the figure look a little better: %! ## - scale and label the axes %! ## - show gridlines %! xlim ([0 15]); %! ylim ([0 15]); %! xlabel ('Feature 1'); %! ylabel ('Feature 2'); %! grid %! hold %! %! ## Calculate and print the three validity measures. %! printf ("Partition Coefficient: %f\n", ... %! partition_coeff (soft_partition)); %! printf ("Partition Entropy (with a = 2): %f\n", ... %! partition_entropy (soft_partition, 2)); %! printf ("Xie-Beni Index: %f\n\n", ... %! xie_beni_index (input_data, cluster_centers, ... %! soft_partition)); ##---------------------------------------------------------------------- ## FCM Demo #2 ##---------------------------------------------------------------------- %!demo %! ## This demo: %! ## - classifies three-dimensional unlabeled data points using %! ## the Fuzzy C-Means algorithm into three fuzzy clusters %! ## - plots the input points together with the cluster centers %! ## - evaluates the quality of the resulting clusters using %! ## three validity measures: the partition coefficient, the %! ## partition entropy, and the Xie-Beni validity index %! ## %! ## Note: The input_data was selected to form three areas of %! ## different shapes. %! %! ## Use fcm to classify the input_data. %! input_data = [1 11 5; 1 12 6; 1 13 5; 2 11 7; 2 12 6; 2 13 7; %! 3 11 6; 3 12 5; 3 13 7; 1 1 10; 1 3 9; 2 2 11; %! 3 1 9; 3 3 10; 3 5 11; 4 4 9; 4 6 8; 5 5 8; 5 7 9; %! 6 6 10; 9 10 12; 9 12 13; 9 13 14; 10 9 13; 10 13 12; %! 11 10 14; 11 12 13; 12 6 12; 12 7 15; 12 9 15; %! 14 6 14; 14 8 13]; %! number_of_clusters = 3; %! [cluster_centers, soft_partition, obj_fcn_history] = ... %! fcm (input_data, number_of_clusters, [NaN NaN NaN 0]) %! %! ## Plot the data points in two dimensions (using features 1 & 2) %! ## as small blue x's. %! figure ('NumberTitle', 'off', 'Name', 'FCM Demo 2'); %! for i = 1 : rows (input_data) %! plot (input_data(i, 1), input_data(i, 2), 'LineWidth', 2, ... %! 'marker', 'x', 'color', 'b'); %! hold on; %! endfor %! %! ## Plot the cluster centers in two dimensions %! ## (using features 1 & 2) as larger red *'s. %! for i = 1 : number_of_clusters %! plot (cluster_centers(i, 1), cluster_centers(i, 2), ... %! 'LineWidth', 4, 'marker', '*', 'color', 'r'); %! hold on; %! endfor %! %! ## Make the figure look a little better: %! ## - scale and label the axes %! ## - show gridlines %! xlim ([0 15]); %! ylim ([0 15]); %! xlabel ('Feature 1'); %! ylabel ('Feature 2'); %! grid %! hold %! %! ## Plot the data points in two dimensions %! ## (using features 1 & 3) as small blue x's. %! figure ('NumberTitle', 'off', 'Name', 'FCM Demo 2'); %! for i = 1 : rows (input_data) %! plot (input_data(i, 1), input_data(i, 3), 'LineWidth', 2, ... %! 'marker', 'x', 'color', 'b'); %! hold on; %! endfor %! %! ## Plot the cluster centers in two dimensions %! ## (using features 1 & 3) as larger red *'s. %! for i = 1 : number_of_clusters %! plot (cluster_centers(i, 1), cluster_centers(i, 3), ... %! 'LineWidth', 4, 'marker', '*', 'color', 'r'); %! hold on; %! endfor %! %! ## Make the figure look a little better: %! ## - scale and label the axes %! ## - show gridlines %! xlim ([0 15]); %! ylim ([0 15]); %! xlabel ('Feature 1'); %! ylabel ('Feature 3'); %! grid %! hold %! %! ## Calculate and print the three validity measures. %! printf ("Partition Coefficient: %f\n", ... %! partition_coeff (soft_partition)); %! printf ("Partition Entropy (with a = 2): %f\n", ... %! partition_entropy (soft_partition, 2)); %! printf ("Xie-Beni Index: %f\n\n", ... %! xie_beni_index (input_data, cluster_centers, ... %! soft_partition)); ## Test input validation %!error %! fcm() %!error %! fcm(1) %!error %! fcm(1, 2, 3, 4) %!error %! fcm('input', 2) %!error %! fcm(1, 0) %!error %! fcm(1, 2, 2j) fuzzy-logic-toolkit-0.6.1/inst/gauss2mf.m000066400000000000000000000126021466512601400203530ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} gauss2mf (@var{x}, @var{params}) ## @deftypefnx {Function File} {@var{y} =} gauss2mf (@var{[x1 x2 ... xn]}, @var{[sig1 c1 sig2 c2]}) ## ## For a given domain @var{x} and parameters @var{params} (or ## @var{[sig1 c1 sig2 c2]}), return the corresponding @var{y} values for the ## two-sided Gaussian composite membership function. This membership function is ## a smooth curve calculated from two Gaussian membership functions as follows: ## ## Given parameters @var{sig1}, @var{c1}, @var{sig2}, and @var{c2}, that define ## two Gaussian membership functions, let: ## ## @verbatim ## f1(x) = exp((-(x - c1)^2)/(2 * sig1^2)) if x <= c1 ## 1 otherwise ## ## f2(x) = 1 if x <= c2 ## exp((-(x - c2)^2)/(2 * sig2^2)) otherwise ## @end verbatim ## ## Then gauss2mf is given by: ## ## @verbatim ## f(x) = f1(x) * f2(x) ## @end verbatim ## ## The argument @var{x} must be a real number or a non-empty vector of strictly ## increasing real numbers, and @var{sig1}, @var{c1}, @var{sig2}, and @var{c2} ## must be real numbers. ## Gauss2mf always returns a continuously differentiable curve with values in ## the range [0, 1]. ## ## If @var{c1} < @var{c2}, gauss2mf is a normal membership function (has a ## maximum value of 1), with the rising curve identical to that of f1(x) and a ## falling curve identical to that of f2(x), above. If @var{c1} >= @var{c2}, ## gauss2mf returns a subnormal membership function (has a maximum value less ## than 1). ## ## To run the demonstration code, type "@t{demo gauss2mf}" (without the quotation ## marks) at the Octave prompt. ## ## @seealso{dsigmf, gaussmf, gbellmf, pimf, psigmf, sigmf, smf, trapmf, trimf, zmf} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy membership gaussian ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: gauss2mf.m ## Last-Modified: 13 Jun 2024 function y = gauss2mf (x, params) ## If the caller did not supply 2 argument values with the correct ## types, print an error message and halt. if (nargin != 2) error ("gauss2mf requires 2 arguments\n"); elseif (!is_domain (x)) error ("gauss2mf's first argument must be a valid domain\n"); elseif (!are_mf_params ('gauss2mf', params)) error ("gauss2mf's second argument must be a parameter vector\n"); endif ## Calculate and return the y values of the membership function on ## the domain x according to the definition of gauss2mf given in the ## comment above. sig1 = params(1); c1 = params(2); sig2 = params(3); c2 = params(4); f1_val = @(x_val) (x_val <= c1) * ... exp ((-(x_val - c1)^2)/(2 * sig1^2)) + ... (x_val > c1); f2_val = @(x_val) (x_val <= c2) + ... (x_val > c2) * exp ((-(x_val - c2)^2)/(2 * sig2^2)); f1 = arrayfun (f1_val, x); f2 = arrayfun (f2_val, x); y = f1 .* f2; endfunction %!demo %! x = -10:0.2:10; %! params = [3 0 1.5 2]; %! y1 = gauss2mf(x, params); %! params = [1.5 0 3 2]; %! y2 = gauss2mf(x, params); %! params = [1.5 2 3 0]; %! y3 = gauss2mf(x, params); %! figure('NumberTitle', 'off', 'Name', 'gauss2mf demo'); %! plot(x, y1, 'r;params = [3 0 1.5 2];', 'LineWidth', 2); %! hold on ; %! plot(x, y2, 'b;params = [1.5 0 3 2];', 'LineWidth', 2); %! hold on ; %! plot(x, y3, 'g;params = [1.5 2 3 0];', 'LineWidth', 2); %! ylim([-0.1 1.1]); %! xlabel('Crisp Input Value', 'FontWeight', 'bold'); %! ylabel('Degree of Membership', 'FontWeight', 'bold'); %! grid; %! hold; %!test %! x = -10:2:10; %! params = [3 0 1.5 2]; %! y = [3.8659e-03 0.028566 0.1353 0.4111 0.8007 1 ... %! 1 0.4111 0.028566 3.3546e-04 6.6584e-07]; %! z = gauss2mf(x, params); %! assert(z, y, 1e-4); ## Test input validation %!error %! gauss2mf() %!error %! gauss2mf(1) %!error %! gauss2mf(1, 2, 3) %!error %! gauss2mf([1 0], 2) %!error %! gauss2mf(1, 2) %!error %! gauss2mf(0:100, []) %!error %! gauss2mf(0:100, [30]) %!error %! gauss2mf(0:100, [2 3]) %!error %! gauss2mf(0:100, [90 80 30]) %!error %! gauss2mf(0:100, 'abc') fuzzy-logic-toolkit-0.6.1/inst/gaussmf.m000066400000000000000000000112551466512601400202740ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} gaussmf (@var{x}, @var{params}) ## @deftypefnx {Function File} {@var{y} =} gaussmf (@var{[x1 x2 ... xn]}, @var{[sig c]}) ## ## For a given domain @var{x} and parameters @var{params} (or @var{[sig c]}), ## return the corresponding @var{y} values for the Gaussian membership ## function. This membership function is shaped like the Gaussian (normal) ## distribution, but scaled to have a maximum value of 1. By contrast, the ## area under the Gaussian distribution curve is 1. ## ## The argument @var{x} must be a real number or a non-empty vector of strictly ## increasing real numbers, and @var{sig} and @var{c} must be real numbers. ## This membership function satisfies the equation: ## ## @verbatim ## f(x) = exp((-(x - c)^2)/(2 * sig^2)) ## @end verbatim ## ## which always returns values in the range [0, 1]. ## ## Just as for the Gaussian (normal) distribution, the parameters @var{sig} and ## @var{c} represent: ## ## @verbatim ## sig^2 == the variance (a measure of the width of the curve) ## c == the center (the mean; the x value of the peak) ## @end verbatim ## ## For larger values of @var{sig}, the curve is flatter, and for smaller values ## of sig, the curve is narrower. The @var{y} value at the center is always 1: ## ## @verbatim ## f(c) == 1 ## @end verbatim ## ## To run the demonstration code, type "@t{demo gaussmf}" (without the quotation ## marks) at the Octave prompt. ## ## @seealso{dsigmf, gauss2mf, gbellmf, pimf, psigmf, sigmf, smf, trapmf, trimf, zmf} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy membership gaussian ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: gaussmf.m ## Last-Modified: 13 Jun 2024 function y = gaussmf (x, params) ## If the caller did not supply 2 argument values with the correct ## types, print an error message and halt. if (nargin != 2) error ("gaussmf requires 2 arguments\n"); elseif (!is_domain (x)) error ("gaussmf's first argument must be a valid domain\n"); elseif (!are_mf_params ('gaussmf', params)) error ("gaussmf's second argument must be a parameter vector\n"); endif ## Calculate and return the y values of the membership function on the ## domain x. sig = params(1); c = params(2); y_val = @(x_val) exp ((-(x_val - c)^2)/(2 * sig^2)); y = arrayfun (y_val, x); endfunction %!demo %! x = -5:0.1:5; %! params = [0.5 0]; %! y1 = gaussmf(x, params); %! params = [1 0]; %! y2 = gaussmf(x, params); %! params = [2 0]; %! y3 = gaussmf(x, params); %! figure('NumberTitle', 'off', 'Name', 'gaussmf demo'); %! plot(x, y1, 'r;params = [0.5 0];', 'LineWidth', 2); %! hold on ; %! plot(x, y2, 'b;params = [1 0];', 'LineWidth', 2); %! hold on ; %! plot(x, y3, 'g;params = [2 0];', 'LineWidth', 2); %! ylim([-0.1 1.1]); %! xlabel('Crisp Input Value'); %! ylabel('Degree of Membership'); %! grid; %! hold; %!test %! x = -5:5; %! params = [2 0]; %! y = [0.043937 0.1353 0.3247 0.6065 0.8825 1 ... %! 0.8825 0.6065 0.3247 0.1353 0.043937]; %! z = gaussmf(x, params); %! assert(z, y, 1e-4); ## Test input validation %!error %! gaussmf() %!error %! gaussmf(1) %!error %! gaussmf(1, 2, 3) %!error %! gaussmf([1 0], 2) %!error %! gaussmf(1, 2) %!error %! gaussmf(0:100, []) %!error %! gaussmf(0:100, [30]) %!error %! gaussmf(0:100, [2 3 4 5]) %!error %! gaussmf(0:100, [90 80 30]) %!error %! gaussmf(0:100, 'abc') fuzzy-logic-toolkit-0.6.1/inst/gbellmf.m000066400000000000000000000116351466512601400202410ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} gbellmf (@var{x}, @var{params}) ## @deftypefnx {Function File} {@var{y} =} gbellmf (@var{[x1 x2 ... xn]}, @var{[a b c]}) ## ## For a given domain @var{x} and parameters @var{params} (or @var{[a b c]}), ## return the corresponding @var{y} values for the generalized bell-shaped ## membership function. ## ## The argument @var{x} must be a real number or a non-empty vector of strictly ## increasing real numbers, @var{a}, @var{b}, and @var{c} must be real numbers, ## @var{a} must be non-zero, and @var{b} must be an integer. This membership ## function satisfies the equation: ## ## @verbatim ## f(x) = 1/(1 + (abs((x - c)/a))^(2 * b)) ## @end verbatim ## ## which always returns values in the range [0, 1]. ## ## The parameters @var{a}, @var{b}, and @var{c} give: ## ## @verbatim ## a == controls the width of the curve at f(x) = 0.5; ## f(c-a) = f(c+a) = 0.5 ## b == controls the slope of the curve at x = c-a and x = c+a; ## f'(c-a) = b/2a and f'(c+a) = -b/2a ## c == the center of the curve ## @end verbatim ## ## This membership function has a value of 0.5 at the two points c - a and ## c + a, and the width of the curve at f(x) == 0.5 is 2 * |a|: ## ## @verbatim ## f(c - a) == f(c + a) == 0.5 ## 2 * |a| == the width of the curve at f(x) == 0.5 ## @end verbatim ## ## The generalized bell-shaped membership function is continuously ## differentiable and is symmetric about the line x = c. ## ## To run the demonstration code, type "@t{demo gbellmf}" (without the quotation ## marks) at the Octave prompt. ## ## @seealso{dsigmf, gauss2mf, gaussmf, pimf, psigmf, sigmf, smf, trapmf, trimf, zmf} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy membership bell-shaped bell ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: gbellmf.m ## Last-Modified: 13 Jun 2024 function y = gbellmf (x, params) ## If the caller did not supply 2 argument values with the correct ## types, print an error message and halt. if (nargin != 2) error ("gbellmf requires 2 arguments\n"); elseif (!is_domain (x)) error ("gbellmf's first argument must be a valid domain\n"); elseif (!are_mf_params ('gbellmf', params)) error ("gbellmf's second argument must be a parameter vector\n"); endif ## Calculate and return the y values of the membership function on the ## domain x. a = params(1); b = params(2); c = params(3); y_val = @(x_val) 1 / (1 + (abs ((x_val - c)/a))^(2 * b)); y = arrayfun (y_val, x); endfunction %!demo %! x = 0:255; %! params = [20 4 100]; %! y1 = gbellmf(x, params); %! params = [30 3 100]; %! y2 = gbellmf(x, params); %! params = [40 2 100]; %! y3 = gbellmf(x, params); %! figure('NumberTitle', 'off', 'Name', 'gbellmf demo'); %! plot(x, y1, 'r;params = [20 4 100];', 'LineWidth', 2) %! hold on; %! plot(x, y2, 'b;params = [30 3 100];', 'LineWidth', 2) %! hold on; %! plot(x, y3, 'g;params = [40 2 100];', 'LineWidth', 2) %! ylim([-0.1 1.1]); %! xlabel('Crisp Input Value', 'FontWeight', 'bold'); %! ylabel('Degree of Membership', 'FontWeight', 'bold'); %! grid; %!test %! x = 0:25:250; %! params = [40 2 100]; %! y = [0.024961 0.074852 0.2906 0.8676 1 0.8676 ... %! 0.2906 0.074852 0.024961 0.010377 5.0313e-03]; %! z = gbellmf(x, params); %! assert(z, y, 1e-4); ## Test input validation %!error %! gbellmf() %!error %! gbellmf(1) %!error %! gbellmf(1, 2, 3) %!error %! gbellmf([1 0], 2) %!error %! gbellmf(1, 2) %!error %! gbellmf(0:100, []) %!error %! gbellmf(0:100, [30]) %!error %! gbellmf(0:100, [2 3]) %!error %! gbellmf(0:100, [90 80 30 50]) %!error %! gbellmf(0:100, 'abcd') fuzzy-logic-toolkit-0.6.1/inst/gensurf.m000066400000000000000000000204241466512601400202760ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {} gensurf (@var{fis}) ## @deftypefnx {Function File} {} gensurf (@var{fis}, @var{input_axes}) ## @deftypefnx {Function File} {} gensurf (@var{fis}, @var{input_axes}, @var{output_axes}) ## @deftypefnx {Function File} {} gensurf (@var{fis}, @var{input_axes}, @var{output_axes}, @var{grids}) ## @deftypefnx {Function File} {} gensurf (@var{fis}, @var{input_axes}, @var{output_axes}, @var{grids}, @var{ref_input}) ## @deftypefnx {Function File} {} gensurf (@var{fis}, @var{input_axes}, @var{output_axes}, @var{grids}, @var{ref_input}, @var{num_points}) ## @deftypefnx {Function File} {@var{[x, y, z]} =} gensurf (...) ## ## Generate and plot a surface (or 2-dimensional curve) showing one FIS output ## as a function of two (or one) of the FIS inputs. The reference input is used ## for all FIS inputs that are not in the input_axes vector. ## ## Grids, which specifies the number of grids to show on the input axes, may be ## a scalar or a vector of length 2. If a scalar, then both axes will use the ## same number of grids. If a vector of length 2, then the grids on the two axes ## are controlled separately. ## ## Num_points specifies the number of points to use when evaluating the FIS. ## ## The final form "[x, y, z] = gensurf(...)" suppresses plotting. ## ## Default values for arguments not supplied are: ## @itemize @bullet ## @item ## input_axes == [1 2] ## @item ## output_axis == 1 ## @item ## grids == [15 15] ## @item ## ref_input == [] ## @item ## num_points == 101 ## @end itemize ## ## Six demo scripts that use gensurf are: ## @itemize @bullet ## @item ## cubic_approx_demo.m ## @item ## heart_disease_demo_1.m ## @item ## heart_disease_demo_2.m ## @item ## investment_portfolio_demo.m ## @item ## linear_tip_demo.m ## @item ## mamdani_tip_demo.m ## @item ## sugeno_tip_demo.m ## @end itemize ## ## Current limitation: ## The form of gensurf that suppresses plotting (the final form above) is not yet ## implemented. ## ## @seealso{cubic_approx_demo, heart_disease_demo_1, heart_disease_demo_2, investment_portfolio_demo, linear_tip_demo, mamdani_tip_demo, sugeno_tip_demo, plotmf} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis plot ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: gensurf.m ## Last-Modified: 29 May 2024 function [x, y, z] = gensurf (fis, input_axes = [1 2], ... output_axis = 1, grids = [15 15], ... ref_input = [], num_points = 101) ## If gensurf was called with an incorrect number of arguments, ## or the arguments do not have the correct type, print an error ## message and halt. if ((nargin < 1) || (nargin > 6)) error ("gensurf requires between 1 and 6 arguments\n"); elseif (!is_fis (fis)) error ("gensurf's first argument must be an FIS structure\n"); elseif ((nargin >= 2) && !are_input_indices (input_axes, fis)) error ("gensurf's second argument must be valid input indices\n"); elseif ((nargin >= 3) && !is_output_index (output_axis, fis)) error ("gensurf's third argument must be a valid output index\n"); elseif ((nargin >= 4) && !is_grid_spec (grids)) error ("gensurf's 4th argument must be a grid specification\n"); elseif ((nargin >= 5) && !is_ref_input (ref_input, fis, input_axes)) error ("gensurf's 5th argument must be reference input values\n"); elseif ((nargin == 6) && ... !(is_pos_int (num_points) && (num_points >= 2))) error ("gensurf's sixth argument must be an integer >= 2\n"); endif if (length (input_axes) == 1 || columns (fis.input) == 1) generate_plot (fis, input_axes, output_axis, grids, ... ref_input, num_points); else generate_surface (fis, input_axes, output_axis, grids, ... ref_input, num_points); endif endfunction ##---------------------------------------------------------------------- ## Function: generate_plot ## Purpose: Generate a plot representing one of the FIS outputs as a ## function of one of the FIS inputs. ##---------------------------------------------------------------------- function [x, y, z] = generate_plot (fis, input_axis, output_axis, ... grids, ref_input, num_points) ## Create input to FIS using grid points and reference values. num_inputs = columns (fis.input); num_grid_pts = grids(1); fis_input = zeros (num_grid_pts, num_inputs); if (num_inputs == 1) input_axis = 1; endif for i = 1 : num_inputs if (i == input_axis) x_axis = (linspace (fis.input(i).range(1), ... fis.input(i).range(2), ... num_grid_pts))'; fis_input(:, i) = x_axis; else fis_input(:, i) = ref_input(i) * ones (num_grid_pts, 1); endif endfor ## Compute and plot the output. output = evalfis_private (fis_input, fis, num_points); figure ('NumberTitle', 'off', 'Name', fis.name); plot (x_axis, output, 'LineWidth', 2); xlabel (fis.input(input_axis).name, 'FontWeight', 'bold'); ylabel (fis.output(output_axis).name, 'FontWeight', 'bold'); grid; hold; endfunction ##---------------------------------------------------------------------- ## Function: generate_surface ## Purpose: Generate a surface representing one of the FIS outputs as ## a function of two of the FIS inputs. ##---------------------------------------------------------------------- function [x, y, z] = generate_surface (fis, input_axes, output_axis, ... grids, ref_input, num_points) ## Create input to FIS using grid points and reference values. num_inputs = columns (fis.input); if (length (grids) == 1) grids = [grids grids]; endif num_grid_pts = prod (grids); fis_input = zeros (num_grid_pts, num_inputs); for i = 1 : num_inputs if (i == input_axes(1)) x_axis = (linspace (fis.input(i).range(1), ... fis.input(i).range(2), ... grids(1)))'; elseif (i == input_axes(2)) y_axis = (linspace (fis.input(i).range(1), ... fis.input(i).range(2), ... grids(2)))'; else fis_input(:, i) = ref_input(i) * ones (num_grid_pts, 1); endif endfor [xx, yy] = meshgrid (x_axis, y_axis); fis_input(:, input_axes(1)) = xx(:); fis_input(:, input_axes(2)) = yy(:); ## Compute the output and reshape it to fit the grid. output = evalfis_private (fis_input, fis, num_points); z_matrix = reshape (output(:, output_axis), length (x_axis), ... length (y_axis)); ## Plot the surface. figure ('NumberTitle', 'off', 'Name', fis.name); surf (x_axis, y_axis, z_matrix); xlabel (fis.input(input_axes(1)).name); ylabel (fis.input(input_axes(2)).name); zlabel (fis.output(output_axis).name); endfunction %!shared fis %! fis = readfis ('cubic_approximator.fis'); ## Test input validation %!error %! gensurf() %!error %! gensurf(fis, 1, 1, 3, 0, 2, 0) %!error %! gensurf(1) %!error %! gensurf(fis, 2) %!error %! gensurf(fis, 1, 2) %!error %! gensurf(fis, 1, 1, 0) %!error %! gensurf(fis, 1, 1, 3, [0; 0]) fuzzy-logic-toolkit-0.6.1/inst/getfis.m000066400000000000000000000476451466512601400201240ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{retval} =} getfis (@var{fis}) ## @deftypefnx {Function File} {@var{retval} =} getfis (@var{fis}, @var{property}) ## @deftypefnx {Function File} {@var{retval} =} getfis (@var{fis}, @var{in_or_out}, @var{var_index}) ## @deftypefnx {Function File} {@var{retval} =} getfis (@var{fis}, @var{in_or_out}, @var{var_index}, @var{var_property}) ## @deftypefnx {Function File} {@var{retval} =} getfis (@var{fis}, @var{in_or_out}, @var{var_index}, @var{mf}, @var{mf_index}) ## @deftypefnx {Function File} {@var{retval} =} getfis (@var{fis}, @var{in_or_out}, @var{var_index}, @var{mf}, @var{mf_index}, @var{mf_property}) ## ## Return or print the property (field) values of an FIS structure ## specified by the arguments. ## ## There are six forms of getfis: ## ## @multitable @columnfractions .20 .70 ## @headitem Number of Arguments @tab Action Taken ## @item 1 ## @tab Print (some) properties of an FIS structure on standard output. ## Return the empty set. ## @item 2 ## @tab Return a specified property of the FIS structure. The properties ## that may be specified are: name, type, version, numinputs, ## numoutputs, numinputmfs, numoutputmfs, numrules, andmethod, ## ormethod, impmethod, addmethod, defuzzmethod, inlabels, outlabels, ## inrange, outrange, inmfs, outmfs, inmflabels, outmflabels, ## inmftypes, outmftypes, inmfparams, outmfparams, and rulelist. ## @item 3 ## @tab Print the properties of a specified input or output variable ## of the FIS structure. Return the empty set. ## @item 4 ## @tab Return a specified property of an input or output variable. ## The properties that may be specified are: name, range, nummfs, ## and mflabels. ## @item 5 ## @tab Print the properties of a specified membership function of the ## FIS structure. Return the empty set. ## @item 6 ## @tab Return a specified property of a membership function. The ## properties that may be specified are: name, type, and params. ## @end multitable ## @sp 1 ## The types/values of the arguments are expected to be: ## ## @multitable @columnfractions .20 .70 ## @headitem Argument @tab Expected Type or Value ## @item @var{fis} ## @tab an FIS structure ## @item @var{property} ## @tab a string; one of: 'name', 'type', 'version', 'numinputs', ## 'numoutputs', 'numinputmfs', 'numoutputmfs', ## 'numrules', 'andmethod', 'ormethod', 'impmethod', ## 'addmethod', 'defuzzmethod' 'inlabels', 'outlabels', ## 'inrange', 'outrange', 'inmfs', 'outmfs', ## 'inmflabels', 'outmflabels', 'inmftypes', ## 'outmftypes', 'inmfparams', 'outmfparams', and ## 'rulelist' (case-insensitive) ## @item @var{in_or_out} ## @tab either 'input' or 'output' (case-insensitive) ## @item @var{var_index} ## @tab a valid integer index of an input or output FIS variable ## @item @var{var_property} ## @tab a string; one of: 'name', 'range', 'nummfs', and 'mflabels' ## @item @var{mf} ## @tab the string 'mf' ## @item @var{mf_index} ## @tab a valid integer index of a membership function ## @item @var{mf_property} ## @tab a string; one of 'name', 'type', or 'params' ## @end multitable ## @sp 1 ## Note that all of the strings representing properties above are case ## insensitive. ## ## @seealso{setfis, showfis} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: getfis.m ## Last-Modified: 13 Jun 2024 ##---------------------------------------------------------------------- function retval = getfis (fis, arg2 = 'dummy', arg3 = 'dummy', ... arg4 = 'dummy', arg5 = 'dummy', ... arg6 = 'dummy') switch (nargin) case 1 retval = getfis_one_arg (fis); case 2 retval = getfis_two_args (fis, arg2); case 3 retval = getfis_three_args (fis, arg2, arg3); case 4 retval = getfis_four_args (fis, arg2, arg3, arg4); case 5 retval = getfis_five_args (fis, arg2, arg3, arg4, arg5); case 6 retval = getfis_six_args (fis, arg2, arg3, arg4, arg5, ... arg6); otherwise error ("getfis requires 1-6 arguments\n"); endswitch endfunction ##---------------------------------------------------------------------- ## Function: getfis_one_arg ## Purpose: Handle calls to getfis that have 1 argument. See the ## comment at the top of this file for more complete info. ##---------------------------------------------------------------------- function retval = getfis_one_arg (fis) ## If the argument does not have the correct type, print an error ## message and halt. if (!is_fis (fis)) error ("the first argument to getfis must be an FIS structure\n"); endif ## Print (some) properties of the FIS structure. Return the empty set. printf ("Name = %s\n", fis.name); printf ("Type = %s\n", fis.type); printf ("NumInputs = %d\n", columns(fis.input)); printf ("InLabels = \n"); for i = 1 : columns (fis.input) printf ("\t%s\n", fis.input(i).name); endfor printf ("NumOutputs = %d\n", columns(fis.output)); printf ("OutLabels = \n"); for i = 1 : columns (fis.output) printf ("\t%s\n", fis.output(i).name); endfor printf ("NumRules = %d\n", columns(fis.rule)); printf ("AndMethod = %s\n", fis.andMethod); printf ("OrMethod = %s\n", fis.orMethod); printf ("ImpMethod = %s\n", fis.impMethod); printf ("AggMethod = %s\n", fis.aggMethod); printf ("DefuzzMethod = %s\n", fis.defuzzMethod); retval = []; endfunction ##---------------------------------------------------------------------- ## Function: getfis_two_args ## Purpose: Handle calls to getfis that have 2 arguments. See the ## comment at the top of this file for more complete info. ##---------------------------------------------------------------------- function retval = getfis_two_args (fis, arg2) ## If not all of the arguments have the correct types, print an error ## message and halt. if (!is_fis (fis)) error ("the first argument to getfis must be an FIS structure\n"); elseif (!(is_string (arg2) && ismember (tolower (arg2), {'name', ... 'type', 'version', 'numinputs', 'numoutputs', ... 'numinputmfs', 'numoutputmfs', 'numrules', 'andmethod', ... 'ormethod', 'impmethod', 'aggmethod', 'defuzzmethod', ... 'inlabels', 'outlabels', 'inrange', 'outrange', 'inmfs', ... 'outmfs', 'inmflabels', 'outmflabels', 'inmftypes', ... 'outmftypes', 'inmfparams', 'outmfparams', 'rulelist'}))) error ("unknown second argument to getfis\n"); endif ## Return the specified property of the FIS structure. switch (tolower (arg2)) case 'name' retval = fis.name; case 'type' retval = fis.type; case 'version' retval = fis.version; case 'numinputs' retval = columns (fis.input); case 'numoutputs' retval = columns (fis.output); case 'numrules' retval = columns(fis.rule); case 'andmethod' retval = fis.andMethod; case 'ormethod' retval = fis.orMethod; case 'impmethod' retval = fis.impMethod; case 'aggmethod' retval = fis.aggMethod; case 'defuzzmethod' retval = fis.defuzzMethod; case 'numinputmfs' retval = []; for i = 1 : columns (fis.input) if (i == 1) retval = columns(fis.input(i).mf); else retval = [retval columns(fis.input(i).mf)]; endif endfor case 'numoutputmfs' retval = []; for i = 1 : columns (fis.output) if (i == 1) retval = columns(fis.output(i).mf); else retval = [retval columns(fis.output(i).mf)]; endif endfor case 'inlabels' retval = []; for i = 1 : columns (fis.input) if (i == 1) retval = fis.input(i).name; else retval = [retval; fis.input(i).name]; endif endfor case 'outlabels' retval = []; for i = 1 : columns (fis.output) if (i == 1) retval = fis.output(i).name; else retval = [retval; fis.output(i).name]; endif endfor case 'inrange' retval = []; for i = 1 : columns (fis.input) if (i == 1) retval = fis.input(i).range; else retval = [retval; fis.input(i).range]; endif endfor case 'outrange' retval = []; for i = 1 : columns (fis.output) if (i == 1) retval = fis.output(i).range; else retval = [retval; fis.output(i).range]; endif endfor case 'inmfs' retval = []; for i = 1 : columns (fis.input) if (i == 1) retval = columns(fis.input(i).mf); else retval = [retval columns(fis.input(i).mf)]; endif endfor case 'outmfs' retval = []; for i = 1 : columns (fis.output) if (i == 1) retval = columns(fis.output(i).mf); else retval = [retval columns(fis.output(i).mf)]; endif endfor case 'inmflabels' retval = []; for i = 1 : columns (fis.input) for j = 1 : columns (fis.input(i).mf) if (i == 1 && y == 1) retval = fis.input(i).mf(j).name; else retval = [retval; fis.input(i).mf(j).name]; endif endfor endfor case 'outmflabels' retval = []; for i = 1 : columns (fis.output) for j = 1 : columns (fis.output(i).mf) if (i == 1 && y == 1) retval = fis.output(i).mf(j).name; else retval = [retval; fis.output(i).mf(j).name]; endif endfor endfor case 'inmftypes' retval = []; for i = 1 : columns (fis.input) for j = 1 : columns (fis.input(i).mf) if (i == 1 && y == 1) retval = fis.input(i).mf(j).type; else retval = [retval; fis.input(i).mf(j).type]; endif endfor endfor case 'outmftypes' retval = []; for i = 1 : columns (fis.output) for j = 1 : columns (fis.output(i).mf) if (i == 1 && y == 1) retval = fis.output(i).mf(j).type; else retval = [retval; fis.output(i).mf(j).type]; endif endfor endfor case 'inmfparams' ## Determine the dimensions of the matrix to return. max_len = 0; num_inputs = columns (fis.input); num_mfs = 0; for i = 1 : num_inputs num_var_i_mfs = columns (fis.input(i).mf); num_mfs += num_var_i_mfs; for j = 1 : num_var_i_mfs max_len = max (max_len, length (fis.input(i).mf(j).params)); endfor endfor ## Assemble the matrix of params to return. Pad with zeros. retval = zeros (num_mfs, max_len); for i = 1 : num_inputs for j = 1 : columns (fis.input(i).mf) next_row_index = (i - 1) * max_len + j; next_row = fis.input(i).mf(j).params; retval(next_row_index, 1 : length (next_row)) = next_row; endfor endfor case 'outmfparams' ## Determine the dimensions of the matrix to return. max_len = 0; num_outputs = columns (fis.output); num_mfs = 0; for i = 1 : num_outputs num_var_i_mfs = columns (fis.output(i).mf); num_mfs += num_var_i_mfs; for j = 1 : num_var_i_mfs max_len = max (max_len, length (fis.output(i).mf(j).params)); endfor endfor ## Assemble the matrix of params to return. Pad with zeros. retval = zeros (num_mfs, max_len); for i = 1 : num_outputs for j = 1 : columns (fis.output(i).mf) next_row_index = (i - 1) * max_len + j; next_row = fis.output(i).mf(j).params; retval(next_row_index, 1 : length (next_row)) = next_row; endfor endfor case 'rulelist' ## Determine the dimensions of the matrix to return. num_inputs = columns (fis.input); num_outputs = columns (fis.output); num_rules = columns (fis.rule); ## Assemble the matrix of rules to return. retval = zeros (num_rules, num_inputs + num_outputs + 2); for i = 1 : num_rules retval(i, 1:num_inputs) = fis.rule(i).antecedent; retval(i, num_inputs+1:num_inputs+num_outputs) = ... fis.rule(i).consequent; retval(i, num_inputs+num_outputs+1) = fis.rule(i).weight; retval(i, num_inputs+num_outputs+2) = fis.rule(i).connection; endfor otherwise error ("internal error in getfis_two_args"); endswitch endfunction ##---------------------------------------------------------------------- ## Function: getfis_three_args ## Purpose: Handle calls to getfis that have 3 arguments. See the ## comment at the top of this file for more complete info. ##---------------------------------------------------------------------- function retval = getfis_three_args (fis, arg2, arg3) ## If not all of the arguments have the correct types, print an error ## message and halt. if (!is_fis (fis)) error ("the first argument to getfis must be an FIS structure\n"); elseif (!(is_string (arg2) && ... ismember (tolower (arg2), {'input','output'}))) error ("incorrect second argument to getfis\n"); elseif (!is_var_index (fis, arg2, arg3)) error ("incorrect third argument to getfis\n"); endif ## Print the properties of a specified input or output variable of the ## FIS structure. Return the empty set. var_str = ["fis." tolower(arg2) "(" num2str(arg3) ")"]; var_mf_str = [var_str ".mf"]; num_mfs = columns (eval (var_mf_str)); printf ("Name = %s\n", eval ([var_str ".name"])); printf ("NumMFs = %d\n", num_mfs); printf ("MFLabels = \n"); for i = 1 : num_mfs printf ("\t%s\n", eval ([var_mf_str "(" num2str(i) ").name"])); endfor printf ("Range = %s\n", mat2str (eval ([var_str ".range"]))); retval = []; endfunction ##---------------------------------------------------------------------- ## Function: getfis_four_args ## Purpose: Handle calls to getfis that have 4 arguments. See the ## comment at the top of this file for more complete info. ##---------------------------------------------------------------------- function retval = getfis_four_args (fis, arg2, arg3, arg4) ## If not all of the arguments have the correct types, print an error ## message and halt. if (!is_fis (fis)) error ("the first argument to getfis must be an FIS structure\n"); elseif (!(is_string (arg2) && ... ismember (tolower (arg2), {'input','output'}))) error ("incorrect second argument to getfis\n"); elseif (!is_var_index (fis, arg2, arg3)) error ("incorrect third argument to getfis\n"); elseif (!(is_string (arg4) && ismember (tolower (arg4), ... {'name', 'range', 'nummfs', 'mflabels'}))) error ("incorrect fourth argument to getfis\n"); endif ## Return the specified property of the FIS input or output variable. arg2 = tolower (arg2); arg4 = tolower (arg4); if (ismember (arg4, {'name', 'range'})) retval = eval (["fis." arg2 "(" num2str(arg3) ")." arg4]); elseif (strcmp (arg4, 'nummfs')) retval = columns (eval (["fis." arg2 "(" num2str(arg3) ").mf"])); elseif (strcmp (arg2, 'input') && strcmp (arg4, 'mflabels')) retval = []; for i = 1 : columns (fis.input) for j = 1 : columns (fis.input(i).mf) retval = [retval; fis.input(i).mf(j).name]; endfor endfor elseif (strcmp (arg2, 'output') && strcmp (arg4, 'mflabels')) retval = []; for i = 1 : columns (fis.output) for j = 1 : columns (fis.output(i).mf) retval = [retval; fis.output(i).mf(j).name]; endfor endfor endif endfunction ##---------------------------------------------------------------------- ## Function: getfis_five_args ## Purpose: Handle calls to getfis that have 5 arguments. See the ## comment at the top of this file for more complete info. ##---------------------------------------------------------------------- function retval = getfis_five_args (fis, arg2, arg3, arg4, arg5) ## If not all of the arguments have the correct types, print an error ## message and halt. if (!is_fis (fis)) error ("the first argument to getfis must be an FIS structure\n"); elseif (!(is_string(arg2) && ... ismember(tolower(arg2), {'input','output'}))) error ("incorrect second argument to getfis\n"); elseif (!is_var_index(fis, arg2, arg3)) error ("incorrect third argument to getfis\n"); elseif (!(is_string(arg4) && isequal(tolower(arg4), 'mf'))) error ("incorrect fourth argument to getfis\n"); elseif (!is_mf_index(fis, arg2, arg3, arg5)) error ("incorrect fifth argument to getfis\n"); endif ## Print the properties of a specified membership function of the ## FIS structure. Return the empty set. var_mf_str = ["fis." tolower(arg2) "(" num2str(arg3) ").mf(" ... num2str(arg5) ")"]; printf ("Name = %s\n", eval ([var_mf_str ".name"])); printf ("Type = %s\n", eval ([var_mf_str ".type"])); printf ("Params = "); disp (eval ([var_mf_str ".params"])); retval = []; endfunction ##---------------------------------------------------------------------- ## Function: getfis_six_args ## Purpose: Handle calls to getfis that have 6 arguments. See the ## comment at the top of this file for more complete info. ##---------------------------------------------------------------------- function retval = getfis_six_args (fis, arg2, arg3, arg4, arg5, arg6) ## If not all of the arguments have the correct types, print an error ## message and halt. if (!is_fis (fis)) error ("the first argument to getfis must be an FIS structure\n"); elseif (!(is_string (arg2) && ... ismember (tolower (arg2), {'input','output'}))) error ("incorrect second argument to getfis\n"); elseif (!is_var_index (fis, arg2, arg3)) error ("incorrect third argument to getfis\n"); elseif (!(is_string (arg4) && isequal (tolower (arg4), 'mf'))) error ("incorrect fourth argument to getfis\n"); elseif (!is_mf_index (fis, arg2, arg3, arg5)) error ("incorrect fifth argument to getfis\n"); elseif (!(is_string (arg6) && ismember (tolower (arg6), ... {'name', 'type', 'params'}))) error ("incorrect sixth argument to getfis\n"); endif ## Return the specified membership function property. retval = eval (["fis." tolower(arg2) "(" num2str(arg3) ").mf(" ... num2str(arg5) ")." tolower(arg6)]); endfunction %!shared fis %! fis = readfis ('mamdani_tip_calculator.fis'); ## Test input validation %!error %! getfis() %!error %! getfis(1, 2, 3, 4, 5, 6, 7) %!error %! getfis(1, 2, 3, 4, 5, 6) %!error %! getfis(fis, 2, 3, 4, 5, 6) %!error %! getfis(fis, 'input', 3, 4, 5, 6) %!error %! getfis(fis, 'input', 1, 4, 5, 6) %!error %! getfis(fis, 'input', 1, 'mf', 5, 6) %!error %! getfis(fis, 'input', 1, 'mf', 1, 6) fuzzy-logic-toolkit-0.6.1/inst/gustafson_kessel.m000066400000000000000000000421571466512601400222130ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{cluster_centers} =} gustafson_kessel (@var{input_data}, @var{num_clusters}) ## @deftypefnx {Function File} {@var{cluster_centers} =} gustafson_kessel (@var{input_data}, @var{num_clusters}, @var{cluster_volume}) ## @deftypefnx {Function File} {@var{cluster_centers} =} gustafson_kessel (@var{input_data}, @var{num_clusters}, @var{cluster_volume}, @var{options}) ## @deftypefnx {Function File} {@var{cluster_centers} =} gustafson_kessel (@var{input_data}, @var{num_clusters}, @var{cluster_volume}, [@var{m}, @var{max_iterations}, @var{epsilon}, @var{display_intermediate_results}]) ## @deftypefnx {Function File} {[@var{cluster_centers}, @var{soft_partition}, @var{obj_fcn_history}] =} gustafson_kessel (@var{input_data}, @var{num_clusters}) ## @deftypefnx {Function File} {[@var{cluster_centers}, @var{soft_partition}, @var{obj_fcn_history}] =} gustafson_kessel (@var{input_data}, @var{num_clusters}, @var{cluster_volume}) ## @deftypefnx {Function File} {[@var{cluster_centers}, @var{soft_partition}, @var{obj_fcn_history}] =} gustafson_kessel (@var{input_data}, @var{num_clusters}, @var{cluster_volume}, @var{options}) ## @deftypefnx {Function File} {[@var{cluster_centers}, @var{soft_partition}, @var{obj_fcn_history}] =} gustafson_kessel (@var{input_data}, @var{num_clusters}, @var{cluster_volume}, [@var{m}, @var{max_iterations}, @var{epsilon}, @var{display_intermediate_results}]) ## ## Using the Gustafson-Kessel algorithm, calculate and return the soft partition ## of a set of unlabeled data points. ## ## Also, if @var{display_intermediate_results} is true, display intermediate ## results after each iteration. Note that because the initial cluster ## prototypes are randomly selected locations in the ranges determined by the ## input data, the results of this function are nondeterministic. ## ## The required arguments to gustafson_kessel are: ## @itemize @w ## @item ## @var{input_data}: a matrix of input data points; each row corresponds to one point ## @item ## @var{num_clusters}: the number of clusters to form ## @end itemize ## ## The third (optional) argument to gustafson_kessel is a vector of cluster volumes. ## If omitted, a vector of 1's will be used as the default. ## ## The fourth (optional) argument to gustafson_kessel is a vector consisting of: ## @itemize @w ## @item ## @var{m}: the parameter (exponent) in the objective function; default = 2.0 ## @item ## @var{max_iterations}: the maximum number of iterations before stopping; default = 100 ## @item ## @var{epsilon}: the stopping criteria; default = 1e-5 ## @item ## @var{display_intermediate_results}: if 1, display results after each iteration, and if 0, do not; default = 1 ## @end itemize ## ## The default values are used if any of the four elements of the vector are missing or ## evaluate to NaN. ## ## The return values are: ## @itemize @w ## @item ## @var{cluster_centers}: a matrix of the cluster centers; each row corresponds to one point ## @item ## @var{soft_partition}: a constrained soft partition matrix ## @item ## @var{obj_fcn_history}: the values of the objective function after each iteration ## @end itemize ## ## Three important matrices used in the calculation are X (the input points ## to be clustered), V (the cluster centers), and Mu (the membership of each ## data point in each cluster). Each row of X and V denotes a single point, ## and Mu(i, j) denotes the membership degree of input point X(j, :) in the ## cluster having center V(i, :). ## ## X is identical to the required argument @var{input_data}; V is identical ## to the output @var{cluster_centers}; and Mu is identical to the output ## @var{soft_partition}. ## ## If n denotes the number of input points and k denotes the number of ## clusters to be formed, then X, V, and Mu have the dimensions: ## ## @verbatim ## 1 2 ... #features ## 1 [[ ] ## X = input_data = 2 [ ] ## ... [ ] ## n [ ]] ## ## 1 2 ... #features ## 1 [[ ] ## V = cluster_centers = 2 [ ] ## ... [ ] ## k [ ]] ## ## 1 2 ... n ## 1 [[ ] ## Mu = soft_partition = 2 [ ] ## ... [ ] ## k [ ]] ## @end verbatim ## ## @seealso{fcm, partition_coeff, partition_entropy, xie_beni_index} ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy partition clustering ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: gustafson_kessel.m ## Last-Modified: 13 Jun 2024 function [cluster_centers, soft_partition, obj_fcn_history] = ... gustafson_kessel (input_data, num_clusters, ... cluster_volume = [], options = [2.0, 100, 1e-5, 1]) ## If gustafson_kessel was called with an incorrect number of ## arguments, or the arguments do not have the correct type, print ## an error message and halt. if ((nargin < 2) || (nargin > 4)) error ("gustafson_kessel requires 2, 3, or 4 arguments\n"); elseif (!is_real_matrix (input_data)) error ("gustafson_kessel's 1st argument must be matrix of reals\n"); elseif (!(is_int (num_clusters) && (num_clusters > 1))) error ("gustafson_kessel's 2nd argument must be an int greater than 1\n"); elseif (!(isequal (cluster_volume, []) || ... (isreal (cluster_volume) && isvector (cluster_volume)))) error ("gustafson_kessel's 3rd arg must be a vector of reals\n"); elseif (!(isreal (options) && isvector (options))) error ("gustafson_kessel's 4th arg must be a vector of reals\n"); endif ## If the cluster volume matrix was not entered, create a default ## value (a vector of 1's). if (isequal (cluster_volume, [])) cluster_volume = ones (1, num_clusters); endif ## Assign options to the more readable variable names: m, ## max_iterations, epsilon, and display_intermediate_results. ## If options are missing or NaN (not a number), use the default ## values. default_options = [2.0, 100, 1e-5, 1]; for i = 1 : 4 if ((length (options) < i) || ... isna (options(i)) || isnan (options(i))) options(i) = default_options(i); endif endfor m = options(1); max_iterations = options(2); epsilon = options(3); display_intermediate_results = options(4); ## Call a private function to compute the output. [cluster_centers, soft_partition, obj_fcn_history] = ... gustafson_kessel_private (input_data, num_clusters, ... cluster_volume, m, max_iterations, ... epsilon, display_intermediate_results); endfunction ##---------------------------------------------------------------------- ## Function: gustafson_kessel_private ## Purpose: Classify unlabeled data points using the Gustafson-Kessel ## algorithm. ## Note: This function (gustafson_kessel_private) is an ## implementation of Algorithm 4.2 in Fuzzy and Neural ## Control, by Robert Babuska, November 2009, p. 69. ##---------------------------------------------------------------------- function [V, Mu, obj_fcn_history] = ... gustafson_kessel_private (X, k, cluster_volume, m, max_iterations, ... epsilon, display_intermediate_results) ## Initialize the prototypes and the calculation. V = init_cluster_prototypes (X, k); obj_fcn_history = zeros (max_iterations); convergence_criterion = epsilon + 1; iteration = 0; ## Calculate a few numbers here to reduce redundant computation. k = rows (V); n = rows (X); sqr_dist = square_distance_matrix (X, V); ## Loop until the objective function is within tolerance or the ## maximum number of iterations has been reached. while (convergence_criterion > epsilon && ... ++iteration <= max_iterations) V_previous = V; Mu = update_cluster_membership (V, X, m, k, n, sqr_dist); Mu_m = Mu .^ m; V = update_cluster_prototypes (Mu_m, X, k); sqr_dist = gk_square_distance_matrix (X, V, Mu_m, cluster_volume); obj_fcn_history(iteration) = ... compute_cluster_obj_fcn (Mu_m, sqr_dist); if (display_intermediate_results) printf ("Iteration count = %d, Objective fcn = %8.6f\n", ... iteration, obj_fcn_history(iteration)); endif convergence_criterion = ... compute_cluster_convergence (V, V_previous); endwhile ## Remove extraneous entries from the tail of the objective ... ## function history. if (convergence_criterion <= epsilon) obj_fcn_history = obj_fcn_history(1 : iteration); endif endfunction ##---------------------------------------------------------------------- ## Function: gk_square_distance_matrix ##---------------------------------------------------------------------- function sqr_dist = gk_square_distance_matrix (X, V, Mu_m, ... cluster_volume) k = rows (V); n = rows (X); num_features = columns (X); sqr_dist = zeros (k, n); for i = 1 : k Vi = V(i, :); covariance_matrix = compute_covariance_matrix (X, V, Mu_m, i); for j = 1 : n Vi_to_Xj = X(j, :) - Vi; A = cluster_volume(i) * ... det (covariance_matrix) ^ (1.0 / num_features) * ... inv (covariance_matrix); sqr_dist(i, j) = sum (Vi_to_Xj .* (A * Vi_to_Xj')'); endfor endfor endfunction ##---------------------------------------------------------------------- ## Function: compute_covariance_matrix ##---------------------------------------------------------------------- function covariance_matrix = compute_covariance_matrix (X, V, Mu_m, i) num_features = columns (V); n = rows (X); num = zeros (num_features); denom = 0.0; Vi = V(i, :); for j = 1 : n Vi_to_Xj = X(j, :) - Vi; num += Mu_m(i, j) * Vi_to_Xj' * Vi_to_Xj; denom += Mu_m(i, j); endfor covariance_matrix = num / denom; endfunction ##---------------------------------------------------------------------- ## Gustafson-Kessel Demo #1 ##---------------------------------------------------------------------- %!demo %! ## This demo: %! ## - classifies a small set of unlabeled data points using %! ## the Gustafson-Kessel algorithm into two fuzzy clusters %! ## - plots the input points together with the cluster centers %! ## - evaluates the quality of the resulting clusters using %! ## three validity measures: the partition coefficient, the %! ## partition entropy, and the Xie-Beni validity index %! ## %! ## Note: The input_data is taken from Chapter 13, Example 17 in %! ## Fuzzy Logic: Intelligence, Control and Information, by %! ## J. Yen and R. Langari, Prentice Hall, 1999, page 381 %! ## (International Edition). %! %! ## Use gustafson_kessel to classify the input_data. %! input_data = [2 12; 4 9; 7 13; 11 5; 12 7; 14 4]; %! number_of_clusters = 2; %! [cluster_centers, soft_partition, obj_fcn_history] = ... %! gustafson_kessel (input_data, number_of_clusters) %! %! ## Plot the data points as small blue x's. %! figure ('NumberTitle', 'off', 'Name', 'Gustafson-Kessel Demo 1'); %! for i = 1 : rows (input_data) %! plot (input_data(i, 1), input_data(i, 2), 'LineWidth', 2, ... %! 'marker', 'x', 'color', 'b'); %! hold on; %! endfor %! %! ## Plot the cluster centers as larger red *'s. %! for i = 1 : number_of_clusters %! plot (cluster_centers(i, 1), cluster_centers(i, 2), ... %! 'LineWidth', 4, 'marker', '*', 'color', 'r'); %! hold on; %! endfor %! %! ## Make the figure look a little better: %! ## - scale and label the axes %! ## - show gridlines %! xlim ([0 15]); %! ylim ([0 15]); %! xlabel ('Feature 1'); %! ylabel ('Feature 2'); %! grid %! hold %! %! ## Calculate and print the three validity measures. %! printf ("Partition Coefficient: %f\n", ... %! partition_coeff (soft_partition)); %! printf ("Partition Entropy (with a = 2): %f\n", ... %! partition_entropy (soft_partition, 2)); %! printf ("Xie-Beni Index: %f\n\n", ... %! xie_beni_index (input_data, cluster_centers, ... %! soft_partition)); ##---------------------------------------------------------------------- ## Gustafson-Kessel Demo #2 ##---------------------------------------------------------------------- %!demo %! ## This demo: %! ## - classifies three-dimensional unlabeled data points using %! ## the Gustafson-Kessel algorithm into three fuzzy clusters %! ## - plots the input points together with the cluster centers %! ## - evaluates the quality of the resulting clusters using %! ## three validity measures: the partition coefficient, the %! ## partition entropy, and the Xie-Beni validity index %! ## %! ## Note: The input_data was selected to form three areas of %! ## different shapes. %! %! ## Use gustafson_kessel to classify the input_data. %! input_data = [1 11 5; 1 12 6; 1 13 5; 2 11 7; 2 12 6; 2 13 7; %! 3 11 6; 3 12 5; 3 13 7; 1 1 10; 1 3 9; 2 2 11; %! 3 1 9; 3 3 10; 3 5 11; 4 4 9; 4 6 8; 5 5 8; 5 7 9; %! 6 6 10; 9 10 12; 9 12 13; 9 13 14; 10 9 13; 10 13 12; %! 11 10 14; 11 12 13; 12 6 12; 12 7 15; 12 9 15; %! 14 6 14; 14 8 13]; %! number_of_clusters = 3; %! [cluster_centers, soft_partition, obj_fcn_history] = ... %! gustafson_kessel (input_data, number_of_clusters, [1 1 1], ... %! [NaN NaN NaN 0]) %! %! ## Plot the data points in two dimensions (using features 1 & 2) %! ## as small blue x's. %! figure ('NumberTitle', 'off', 'Name', 'Gustafson-Kessel Demo 2'); %! for i = 1 : rows (input_data) %! plot (input_data(i, 1), input_data(i, 2), 'LineWidth', 2, ... %! 'marker', 'x', 'color', 'b'); %! hold on; %! endfor %! %! ## Plot the cluster centers in two dimensions %! ## (using features 1 & 2) as larger red *'s. %! for i = 1 : number_of_clusters %! plot (cluster_centers(i, 1), cluster_centers(i, 2), ... %! 'LineWidth', 4, 'marker', '*', 'color', 'r'); %! hold on; %! endfor %! %! ## Make the figure look a little better: %! ## - scale and label the axes %! ## - show gridlines %! xlim ([0 15]); %! ylim ([0 15]); %! xlabel ('Feature 1'); %! ylabel ('Feature 2'); %! grid %! %! ## Plot the data points in two dimensions %! ## (using features 1 & 3) as small blue x's. %! figure ('NumberTitle', 'off', 'Name', 'Gustafson-Kessel Demo 2'); %! for i = 1 : rows (input_data) %! plot (input_data(i, 1), input_data(i, 3), 'LineWidth', 2, ... %! 'marker', 'x', 'color', 'b'); %! hold on; %! endfor %! %! ## Plot the cluster centers in two dimensions %! ## (using features 1 & 3) as larger red *'s. %! for i = 1 : number_of_clusters %! plot (cluster_centers(i, 1), cluster_centers(i, 3), ... %! 'LineWidth', 4, 'marker', '*', 'color', 'r'); %! hold on; %! endfor %! %! ## Make the figure look a little better: %! ## - scale and label the axes %! ## - show gridlines %! xlim ([0 15]); %! ylim ([0 15]); %! xlabel ('Feature 1'); %! ylabel ('Feature 3'); %! grid %! hold %! %! ## Calculate and print the three validity measures. %! printf ("Partition Coefficient: %f\n", ... %! partition_coeff (soft_partition)); %! printf ("Partition Entropy (with a = 2): %f\n", ... %! partition_entropy (soft_partition, 2)); %! printf ("Xie-Beni Index: %f\n\n", ... %! xie_beni_index (input_data, cluster_centers, ... %! soft_partition)); ## Test input validation %!error %! gustafson_kessel() %!error %! gustafson_kessel(1) %!error %! gustafson_kessel(1, 2, 3, 4, 5) %!error %! gustafson_kessel('input', 2) %!error %! gustafson_kessel(1, 0) %!error %! gustafson_kessel(1, 2, 3j) %!error %! gustafson_kessel(1, 2, 3, 4j) fuzzy-logic-toolkit-0.6.1/inst/hamacher_product.m000066400000000000000000000102001466512601400221240ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{retval} =} hamacher_product (@var{x}) ## @deftypefnx {Function File} {@var{retval} =} hamacher_product (@var{x}, @var{y}) ## ## Return the Hamacher product of the input. ## The Hamacher product of two real scalars x and y is: ## (x * y) / (x + y - x * y) ## ## For one vector argument, apply the Hamacher product to all of the elements ## of the vector. (The Hamacher product is associative.) For one ## two-dimensional matrix argument, return a vector of the Hamacher product ## of each column. ## ## For two vectors or matrices of identical dimensions, or for one scalar and ## one vector or matrix argument, return the pairwise Hamacher product. ## ## @seealso{algebraic_product, algebraic_sum, bounded_difference, bounded_sum, drastic_product, drastic_sum, einstein_product, einstein_sum, hamacher_sum} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy hamacher_product ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: hamacher_product.m ## Last-Modified: 26 Jul 2024 function retval = hamacher_product (x, y = 0) if (nargin == 0 || nargin > 2 || !is_real_matrix (x) || !is_real_matrix (y)) error ("invalid arguments to function hamacher_product\n"); elseif (nargin == 1) if (isvector (x)) retval = vector_arg (x); elseif (ndims (x) == 2) retval = matrix_arg (x); else error ("invalid arguments to function hamacher_product\n"); endif elseif (nargin == 2) if (isequal (size (x), size (y))) retval = arrayfun (@scalar_args, x, y); elseif (isscalar (x) && ismatrix (y)) x = x * ones (size (y)); retval = arrayfun (@scalar_args, x, y); elseif (ismatrix (x) && isscalar (y)) y = y * ones (size (x)); retval = arrayfun (@scalar_args, x, y); else error ("invalid arguments to function hamacher_product\n"); endif endif endfunction function retval = scalar_args (x, y) retval = (x * y) / (x + y - x * y); endfunction function retval = vector_arg (real_vector) x = 1; for i = 1 : length (real_vector) y = real_vector(i); if (x == 0 && y == 0) x = 0; else x = (x * y) / (x + y - x * y); endif endfor retval = x; endfunction function retval = matrix_arg (x) num_cols = columns (x); retval = zeros (1, num_cols); for i = 1 : num_cols retval(i) = vector_arg (x(:, i)); endfor endfunction %!test %! x = [5 3]; %! z = hamacher_product(x); %! assert(z, -2.1429, 1e-4); %!test %! x = [5 2 3 6]; %! y = [-1 1 2 3]; %! z = hamacher_product(x, y); %! assert(z, [-0.5556 2.0000 -6.0000 -2.0000], 1e-4); ## Test input validation %!error %! hamacher_product() %!error %! hamacher_product(2j) %!error %! hamacher_product(1, 2j) %!error %! hamacher_product([1 2j]) %!error %! hamacher_product(1, 2, 3) %!error %! hamacher_product([1 2], [1 2 3]) %!error %! hamacher_product([1 2], [1 2; 3 4]) %!error %! hamacher_product(0:100, []) fuzzy-logic-toolkit-0.6.1/inst/hamacher_sum.m000066400000000000000000000100301466512601400212510ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{retval} =} hamacher_sum (@var{x}) ## @deftypefnx {Function File} {@var{retval} =} hamacher_sum (@var{x}, @var{y}) ## ## Return the Hamacher sum of the input. ## The Hamacher sum of two real scalars x and y is: ## (x + y - 2 * x * y) / (1 - x * y) ## ## For one vector argument, apply the Hamacher sum to all of the elements ## of the vector. (The Hamacher sum is associative.) For one ## two-dimensional matrix argument, return a vector of the Hamacher sum ## of each column. ## ## For two vectors or matrices of identical dimensions, or for one scalar and ## one vector or matrix argument, return the pairwise Hamacher sum. ## ## @seealso{algebraic_product, algebraic_sum, bounded_difference, bounded_sum, drastic_product, drastic_sum, einstein_product, einstein_sum, hamacher_product} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy hamacher_sum ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: hamacher_sum.m ## Last-Modified: 26 Jul 2024 function retval = hamacher_sum (x, y = 0) if (nargin == 0 || nargin > 2 || !is_real_matrix (x) || !is_real_matrix (y)) error ("invalid arguments to function hamacher_sum\n"); elseif (nargin == 1) if (isvector (x)) retval = vector_arg (x); elseif (ndims (x) == 2) retval = matrix_arg (x); else error ("invalid arguments to function hamacher_sum\n"); endif elseif (nargin == 2) if (isequal (size (x), size (y))) retval = arrayfun (@scalar_args, x, y); elseif (isscalar (x) && ismatrix (y)) x = x * ones (size (y)); retval = arrayfun (@scalar_args, x, y); elseif (ismatrix (x) && isscalar (y)) y = y * ones (size (x)); retval = arrayfun (@scalar_args, x, y); else error ("invalid arguments to function hamacher_sum\n"); endif endif endfunction function retval = scalar_args (x, y) retval = (x + y - 2 * x * y) / (1 - x * y); endfunction function retval = vector_arg (real_vector) x = 0; for i = 1 : length (real_vector) y = real_vector(i); if (x == 1 && y == 1) x = 1; else x = (x + y - 2 * x * y) / (1 - x * y); endif endfor retval = x; endfunction function retval = matrix_arg (x) num_cols = columns (x); retval = zeros (1, num_cols); for i = 1 : num_cols retval(i) = vector_arg (x(:, i)); endfor endfunction %!test %! x = [5 3]; %! z = hamacher_sum(x); %! assert(z, 1.5714, 1e-4); %!test %! x = [5 2 3 6]; %! y = [-1 1 2 3]; %! z = hamacher_sum(x, y); %! assert(z, [2.3333 1.0000 1.4000 1.5882], 1e-4); ## Test input validation %!error %! hamacher_sum() %!error %! hamacher_sum(2j) %!error %! hamacher_sum(1, 2j) %!error %! hamacher_sum([1 2j]) %!error %! hamacher_sum(1, 2, 3) %!error %! hamacher_sum([1 2], [1 2 3]) %!error %! hamacher_sum([1 2], [1 2; 3 4]) %!error %! hamacher_sum(0:100, []) fuzzy-logic-toolkit-0.6.1/inst/heart_disease_demo_1.m000066400000000000000000000121171466512601400226510ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Script File} {} heart_disease_demo_1 ## ## Demonstrate the use of newfis, addvar, addmf, and addrule ## to build and evaluate an FIS. Also demonstrate the use of the algebraic ## product and sum as the T-norm/S-norm pair, and demonstrate the use of ## hedges in the FIS rules. ## ## The demo: ## @itemize @bullet ## @item ## builds an FIS ## @item ## plots the input membership functions ## @item ## plots the constant output functions ## @item ## displays the FIS rules in verbose format in the Octave window ## @item ## plots the FIS output as a function of the inputs ## @end itemize ## ## @seealso{cubic_approx_demo, heart_disease_demo_2, investment_portfolio_demo, linear_tip_demo, mamdani_tip_demo, sugeno_tip_demo} ## @end deftypefn ## Author: L. Markowsky ## Note: This example is based on an assignment written by ## Dr. Bruce Segee (University of Maine Dept. of ECE). ## Keywords: fuzzy-logic-toolkit fuzzy tests demos ## Directory: fuzzy-logic-toolkit/inst ## Filename: heart_disease_demo_1.m ## Last-Modified: 4 Jun 2024 ## Create new FIS. a = newfis ('Heart-Disease-Risk', 'sugeno', ... 'algebraic_product', 'algebraic_sum', ... 'min', 'max', 'wtaver'); ## Add two inputs and their membership functions. a = addvar (a, 'input', 'LDL-Level', [0 300]); a = addmf (a, 'input', 1, 'Low', 'trapmf', [-1 0 90 130]); a = addmf (a, 'input', 1, 'Moderate', 'trapmf', [90 130 160 200]); a = addmf (a, 'input', 1, 'High', 'trapmf', [160 200 300 301]); a = addvar (a, 'input', 'HDL-Level', [0 100]); a = addmf (a, 'input', 2, 'Low', 'trapmf', [-1 0 35 45]); a = addmf (a, 'input', 2, 'Moderate', 'trapmf', [35 45 55 65]); a = addmf (a, 'input', 2, 'High', 'trapmf', [55 65 100 101]); ## Add one output and its membership functions. a = addvar (a, 'output', 'Heart-Disease-Risk', [-2 12]); a = addmf (a, 'output', 1, 'Negligible', 'constant', 0); a = addmf (a, 'output', 1, 'Low', 'constant', 2.5); a = addmf (a, 'output', 1, 'Medium', 'constant', 5); a = addmf (a, 'output', 1, 'High', 'constant', 7.5); a = addmf (a, 'output', 1, 'Extreme', 'constant', 10); ## Plot the input and output membership functions. plotmf (a, 'input', 1); plotmf (a, 'input', 2); plotmf (a, 'output', 1); ## Add 15 rules and display them in verbose format. a = addrule (a, [1 1 3 1 1; 1 2 2 1 1; 1 3 1 1 1; ... 2 1 4 1 1; 2 2 3 1 1; 2 3 2 1 1; ... 3 1 5 1 1; 3 2 4 1 1; 3 3 3 1 1; ... 1.3 3.3 2 1 2; ... 3.05 1.05 4 1 2; ... -3.2 -1.2 3 1 1]); puts ("\nOutput of showrule(a):\n\n"); showrule (a); ## Plot the output as a function of the two inputs. gensurf (a); %!test %! a = newfis ('Heart-Disease-Risk', 'sugeno', ... %! 'algebraic_product', 'algebraic_sum', ... %! 'min', 'max', 'wtaver'); %! %! ## Add two inputs and their membership functions. %! a = addvar (a, 'input', 'LDL-Level', [0 300]); %! a = addmf (a, 'input', 1, 'Low', 'trapmf', [-1 0 90 130]); %! a = addmf (a, 'input', 1, 'Moderate', 'trapmf', [90 130 160 200]); %! a = addmf (a, 'input', 1, 'High', 'trapmf', [160 200 300 301]); %! %! a = addvar (a, 'input', 'HDL-Level', [0 100]); %! a = addmf (a, 'input', 2, 'Low', 'trapmf', [-1 0 35 45]); %! a = addmf (a, 'input', 2, 'Moderate', 'trapmf', [35 45 55 65]); %! a = addmf (a, 'input', 2, 'High', 'trapmf', [55 65 100 101]); %! %! ## Add one output and its membership functions. %! a = addvar (a, 'output', 'Heart-Disease-Risk', [-2 12]); %! a = addmf (a, 'output', 1, 'Negligible', 'constant', 0); %! a = addmf (a, 'output', 1, 'Low', 'constant', 2.5); %! a = addmf (a, 'output', 1, 'Medium', 'constant', 5); %! a = addmf (a, 'output', 1, 'High', 'constant', 7.5); %! a = addmf (a, 'output', 1, 'Extreme', 'constant', 10); %! %! ## Add 15 rules and display them in verbose format. %! a = addrule (a, [1 1 3 1 1; 1 2 2 1 1; 1 3 1 1 1; ... %! 2 1 4 1 1; 2 2 3 1 1; 2 3 2 1 1; ... %! 3 1 5 1 1; 3 2 4 1 1; 3 3 3 1 1; ... %! 1.3 3.3 2 1 2; ... %! 3.05 1.05 4 1 2; ... %! -3.2 -1.2 3 1 1]); %! %! ldl_hdl = [129 59; 130 60; 90 65; 205 40]; %! heart_disease_risk = evalfis (ldl_hdl, a, 1001); %! assert(heart_disease_risk, [4.2679; 4.1667; 2.5000; 8.3333], 1e-4); fuzzy-logic-toolkit-0.6.1/inst/heart_disease_demo_2.m000066400000000000000000000052741466512601400226600ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Script File} {} heart_disease_demo_2 ## ## Demonstrate the use of the Octave Fuzzy Logic Toolkit to read and evaluate a ## Sugeno-type FIS stored in a file. ## ## The demo: ## @itemize @bullet ## @item ## reads the FIS structure from a file ## @item ## plots the input membership functions ## @item ## plots the (constant) output functions ## @item ## plots the FIS output as a function of the inputs ## @item ## evaluates the Sugeno-type FIS for four inputs ## @end itemize ## ## @seealso{cubic_approx_demo, heart_disease_demo_1, investment_portfolio_demo, linear_tip_demo, mamdani_tip_demo, sugeno_tip_demo} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy tests demos ## Note: This example is based on an assignment written by ## Dr. Bruce Segee (University of Maine Dept. of ECE). ## Directory: fuzzy-logic-toolkit/inst ## Filename: heart_disease_demo_2.m ## Last-Modified: 4 Jun 2024 ## Read the FIS structure from a file. ## (Alternatively, to select heart_disease_risk.fis using the dialog, ## replace the following line with ## fis = readfis (); fis = readfis('heart_disease_risk.fis'); ## Plot the input and output membership functions. plotmf (fis, 'input', 1); plotmf (fis, 'input', 2); plotmf (fis, 'output', 1); ## Plot the Heart Disease Risk as a function of LDL-Level and HDL-Level. gensurf (fis); ## Calculate the Heart Disease Risk for 4 sets of LDL-HDL values: puts ("\nFor the following four sets of LDL-HDL values:\n\n"); ldl_hdl = [129 59; 130 60; 90 65; 205 40] puts ("\nThe Heart Disease Risk is:\n\n"); heart_disease_risk = evalfis (ldl_hdl, fis, 1001) %!test %! fis = readfis ('heart_disease_risk.fis'); %! ldl_hdl = [129 59; 130 60; 90 65; 205 40]; %! heart_disease_risk = evalfis (ldl_hdl, fis, 1001); %! assert(heart_disease_risk, [3.6250; 3.7500; 0; 8.7500], 1e-4); fuzzy-logic-toolkit-0.6.1/inst/heart_disease_risk.fis000066400000000000000000000045061466512601400230050ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fis ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: heart_disease_risk.fis ## Last-Modified: 28 Aug 2012 ## Heart Disease Risk FIS [System] Name = 'Heart-Disease-Risk' Type = 'sugeno' Version = 2.0 NumInputs = 2 NumOutputs = 1 NumRules = 15 AndMethod = 'min' OrMethod = 'max' ImpMethod = 'min' AggMethod = 'max' DefuzzMethod = 'wtaver' [Input1] Name = 'LDL-Level' Range = [0 300] NumMFs = 5 MF1 = 'Low' : 'trapmf', [-1 0 90 110] MF2 = 'Low-Borderline' : 'trapmf', [90 110 120 140] MF3 = 'Borderline' : 'trapmf', [120 140 150 170] MF4 = 'High-Borderline' : 'trapmf', [150 170 180 200] MF5 = 'High' : 'trapmf', [180 200 300 301] [Input2] Name = 'HDL-Level' Range = [0 100] NumMFs = 3 MF1 = 'Low-HDL' : 'trapmf', [-1 0 35 45] MF2 = 'Moderate-HDL' : 'trapmf', [35 45 55 65] MF3 = 'High-HDL' : 'trapmf', [55 65 100 101] [Output1] Name = 'Heart-Disease-Risk' Range = [0 10] NumMFs = 5 MF1 = 'No-Risk' : 'constant', [0] MF2 = 'Low-Risk' : 'constant', [2.5] MF3 = 'Medium-Risk' : 'constant', [5] MF4 = 'High-Risk' : 'constant', [7.5] MF5 = 'Extreme-Risk' : 'constant', [10] [Rules] 1 1, 3 (1) : 1 1 2, 2 (1) : 1 1 3, 1 (1) : 1 2 1, 3 (1) : 1 2 2, 2 (1) : 1 2 3, 2 (1) : 1 3 1, 4 (1) : 1 3 2, 3 (1) : 1 3 3, 2 (1) : 1 4 1, 4 (1) : 1 4 2, 4 (1) : 1 4 3, 3 (1) : 1 5 1, 5 (1) : 1 5 2, 4 (1) : 1 5 3, 3 (1) : 1 fuzzy-logic-toolkit-0.6.1/inst/investment_portfolio.fis000066400000000000000000000032571466512601400234500ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fis ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: investment_portfolio.fis ## Last-Modified: 28 Aug 2012 [System] Name='Investment-Portfolio' Type='mamdani' Version=2.0 NumInputs=2 NumOutputs=1 NumRules=4 AndMethod='einstein_product' OrMethod='einstein_sum' ImpMethod='einstein_product' AggMethod='einstein_sum' DefuzzMethod='centroid' [Input1] Name='Age' Range=[20 100] NumMFs=2 MF1='Young':'zmf',[30 90] MF2='Old':'smf',[30 90] [Input2] Name='Risk-Tolerance' Range=[0 10] NumMFs=2 MF1='Low':'zmf',[2 8] MF2='High':'smf',[2 8] [Output1] Name='Percentage-In-Stocks' Range=[0 100] NumMFs=3 MF1='About-Fifteen':'gaussmf',[10 15] MF2='About-Fifty':'gaussmf',[10 50] MF3='About-Eighty-Five':'gaussmf',[10 85] [Rules] 1 2, 3 (1) : 2 2 1, 1 (1) : 2 -2.3 -1.3, 2 (0.5) : 1 -1.3 -2.3, 2 (0.5) : 1 fuzzy-logic-toolkit-0.6.1/inst/investment_portfolio_demo.m000066400000000000000000000075401466512601400241260ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Script File} {} investment_portfolio_demo ## Demonstrate the use of the Octave Fuzzy Logic Toolkit to read and evaluate ## a Mamdani-type FIS stored in a file. Also demonstrate the use of hedges and ## weights in the FIS rules, the use of the Einstein product and sum as the ## T-norm/S-norm pair, and the non-standard use of the Einstein sum as the ## aggregation method. ## ## The demo: ## @itemize @bullet ## @item ## reads the FIS structure from a file ## @item ## plots the input and output membership functions ## @item ## plots the FIS output as a function of the inputs ## @item ## plots the output of the 4 individual rules for (Age, Risk-Tolerance) = (40, 7) ## @item ## plots the aggregated fuzzy output and the crisp output for ## (Age, Risk-Tolerance) = (40, 7) ## @item ## shows the rules in verbose format in the Octave window ## @end itemize ## ## @seealso{cubic_approx_demo, heart_disease_demo_1, heart_disease_demo_2, linear_tip_demo, mamdani_tip_demo, sugeno_tip_demo} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy tests demos ## Directory: fuzzy-logic-toolkit/inst ## Filename: investment_portfolio_demo.m ## Last-Modified: 4 Jun 2024 ## Read the FIS structure from a file. fis = readfis ('investment_portfolio.fis'); ## Plot the input and output membership functions. plotmf (fis, 'input', 1); plotmf (fis, 'input', 2); plotmf (fis, 'output', 1); ## Plot the Percentage-In-Stocks a function of Age and Risk-Tolerance. gensurf (fis, [1 2], 1); ## Calculate the Percentage-In-Stocks using ## (Age, Risk-Tolerance) = (40, 7). [output, rule_input, rule_output, fuzzy_output] = ... evalfis ([40 7], fis, 1001); ## Plot the output (Percentage-In-Stocks) of the individual fuzzy rules ## on one set of axes. x_axis = linspace (fis.output(1).range(1), ... fis.output(1).range(2), 1001); colors = ['r' 'b' 'm' 'g']; figure ('NumberTitle', 'off', 'Name', ... 'Output of Fuzzy Rules 1-4 for (Age, Risk Tolerance) = (40, 7)'); for i = 1 : 4 y_label = [colors(i) ";Rule " num2str(i) ";"]; plot (x_axis, rule_output(:,i), y_label, 'LineWidth', 2); hold on; endfor ylim ([-0.1, 1.1]); xlabel ('Percentage in Stocks', 'FontWeight', 'bold'); grid; hold; ## Plot the first aggregated fuzzy output and the crisp output ## (Percentage-In-Stocks) on one set of axes. figure('NumberTitle', 'off', 'Name', ... 'Aggregation and Defuzzification for (Age, Risk Tolerace) = (40, 7)'); plot (x_axis, fuzzy_output(:, 1), "b;Aggregated Fuzzy Output;", ... 'LineWidth', 2); hold on; crisp_output = evalmf(x_axis, output(1), 'constant'); y_label = ["r;Crisp Output = " num2str(output(1)) "%;"]; plot (x_axis, crisp_output, y_label, 'LineWidth', 2); ylim ([-0.1, 1.1]); xlabel ('Percentage in Stocks', 'FontWeight', 'bold'); grid; hold; ## Show the rules in English. puts ("\nInvestment Portfolio Calculator Rules:\n\n"); showrule (fis); %!test %! fis = readfis ('investment_portfolio.fis'); %! output = evalfis ([40 7], fis, 1001); %! assert(output, 69.358, 1e-3); fuzzy-logic-toolkit-0.6.1/inst/linear_tip_calculator.fis000066400000000000000000000031731466512601400235130ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fis ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: linear_tip_calculator.fis ## Last-Modified: 28 Aug 2012 [System] Name='Linear-Tip-Calculator' Type='sugeno' Version=2.0 NumInputs=2 NumOutputs=1 NumRules=4 AndMethod='min' OrMethod='max' ImpMethod='min' AggMethod='max' DefuzzMethod='wtaver' [Input1] Name='Food-Quality' Range=[1 10] NumMFs=2 MF1='Bad':'trapmf',[0 1 3 7] MF2='Good':'trapmf',[3 7 10 11] [Input2] Name='Service' Range=[1 10] NumMFs=2 MF1='Bad':'trapmf',[0 1 3 7] MF2='Good':'trapmf',[3 7 10 11] [Output1] Name='Tip' Range=[10 20] NumMFs=3 MF1='Ten-Percent':'linear',[0 0 10] MF2='Fifteen-Percent':'linear',[0 0 15] MF3='Twenty-Percent':'linear',[0 0 20] [Rules] 1 1, 1 (1) : 1 1 2, 2 (1) : 1 2 1, 2 (1) : 1 2 2, 3 (1) : 1 fuzzy-logic-toolkit-0.6.1/inst/linear_tip_demo.m000066400000000000000000000047701466512601400217650ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Script File} {} linear_tip_demo ## ## Demonstrate the use of linear output membership functions to simulate ## constant membership functions. ## ## The demo: ## @itemize @bullet ## @item ## reads the FIS structure from a file ## @item ## plots the input membership functions ## @item ## plots the FIS output as a function of the inputs ## @item ## evaluates the Sugeno-type FIS for six inputs ## @end itemize ## ## @seealso{cubic_approx_demo, heart_disease_demo_1, heart_disease_demo_2, investment_portfolio_demo, mamdani_tip_demo, sugeno_tip_demo} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy tests demos ## Note: This example is based on an assignment written by ## Dr. Bruce Segee (University of Maine Dept. of ECE). ## Directory: fuzzy-logic-toolkit/inst ## Filename: linear_tip_demo.m ## Last-Modified: 4 Jun 2024 ## Read the FIS structure from a file. fis = readfis ('linear_tip_calculator.fis'); ## Plot the input membership functions. plotmf (fis, 'input', 1); plotmf (fis, 'input', 2); ## Plot the Tip as a function of Food-Quality and Service. gensurf (fis); ## Calculate the Tip for 6 sets of input values: puts ("\nFor the following values of (Food Quality, Service):\n\n"); food_service = [1 1; 5 5; 10 10; 4 6; 6 4; 7 4] puts ("\nThe Tip is:\n\n"); tip = evalfis (food_service, fis, 1001) %!test %! fis = readfis ('linear_tip_calculator.fis'); %! food_service = [1 1; 5 5; 10 10; 4 6; 6 4; 7 4]; %! tip = evalfis (food_service, fis, 1001); %! expected_result = ... %! [10.000 %! 15.000 %! 20.000 %! 15.000 %! 15.000 %! 16.250]; %! assert(tip, expected_result, 1e-3); fuzzy-logic-toolkit-0.6.1/inst/mamdani_tip_calculator.fis000066400000000000000000000035561466512601400236540ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fis ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: mamdani_tip_calculator.fis ## Last-Modified: 28 Aug 2012 [System] Name='Mamdani-Tip-Calculator' Type='mamdani' Version=2.0 NumInputs=2 NumOutputs=2 NumRules=4 AndMethod='min' OrMethod='max' ImpMethod='min' AggMethod='max' DefuzzMethod='centroid' [Input1] Name='Food-Quality' Range=[1 10] NumMFs=2 MF1='Bad':'trapmf',[0 1 3 7] MF2='Good':'trapmf',[3 7 10 11] [Input2] Name='Service' Range=[1 10] NumMFs=2 MF1='Bad':'trapmf',[0 1 3 7] MF2='Good':'trapmf',[3 7 10 11] [Output1] Name='Tip' Range=[0 30] NumMFs=3 MF1='About-Ten-Percent':'gaussmf',[2 10] MF2='About-Fifteen-Percent':'gaussmf',[2 15] MF3='About-Twenty-Percent':'gaussmf',[2 20] [Output2] Name='Check-Plus-Tip' Range=[1 1.3] NumMFs=3 MF1='Plus-About-Ten-Percent':'gaussmf',[0.02 1.10] MF2='Plus-About-Fifteen-Percent':'gaussmf',[0.02 1.15] MF3='Plus-About-Twenty-Percent':'gaussmf',[0.02 1.20] [Rules] 1 1, 1 1 (1) : 1 1 2, 2 2 (1) : 1 2 1, 2 2 (1) : 1 2 2, 3 3 (1) : 1 fuzzy-logic-toolkit-0.6.1/inst/mamdani_tip_demo.m000066400000000000000000000100241466512601400221060ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Script File} {} mamdani_tip_demo ## Demonstrate the use of the Octave Fuzzy Logic Toolkit to read and evaluate a ## Mamdani-type FIS stored in a file. ## ## The demo: ## @itemize @bullet ## @item ## reads the FIS structure from a file ## @item ## plots the input and output membership functions ## @item ## plots each of the two FIS outputs as a function of the inputs ## @item ## plots the output of the 4 individual rules for (Food-Quality, Service) = (4, 6) ## @item ## plots the aggregated fuzzy output and the crisp output for ## (Food-Quality, Service) = (4, 6) ## @item ## displays the FIS rules in symbolic format in the Octave window ## @end itemize ## ## @seealso{cubic_approx_demo, heart_disease_demo_1, heart_disease_demo_2, investment_portfolio_demo, linear_tip_demo, sugeno_tip_demo} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy tests demos ## Note: This example is based on an assignment written by ## Dr. Bruce Segee (University of Maine Dept. of ECE). ## Directory: fuzzy-logic-toolkit/inst ## Filename: mamdani_tip_demo.m ## Last-Modified: 4 Jun 2024 ## Read the FIS structure from a file. fis = readfis ('mamdani_tip_calculator.fis'); ## Plot the input and output membership functions. plotmf (fis, 'input', 1); plotmf (fis, 'input', 2); plotmf (fis, 'output', 1); plotmf (fis, 'output', 2); ## Plot the Tip and Check + Tip as functions of Food-Quality ## and Service. gensurf (fis, [1 2], 1); gensurf (fis, [1 2], 2); ## Calculate the Tip and Check + Tip using ## (Food-Quality, Service) = (4, 6). [output, rule_input, rule_output, fuzzy_output] = ... evalfis ([4 6], fis, 1001); ## Plot the first output (Tip) of the individual fuzzy rules ## on one set of axes. x_axis = linspace (fis.output(1).range(1), ... fis.output(1).range(2), 1001); colors = ['r' 'b' 'm' 'g']; figure ('NumberTitle', 'off', 'Name', ... 'Output of Fuzzy Rules 1-4 for Input = (4, 6)'); for i = 1 : 4 y_label = [colors(i) ";Rule " num2str(i) ";"]; plot (x_axis, rule_output(:,i), y_label, 'LineWidth', 2); hold on; endfor ylim ([-0.1, 1.1]); xlabel ('Tip', 'FontWeight', 'bold'); grid; hold; ## Plot the first aggregated fuzzy output and the first crisp output ## (Tip) on one set of axes. figure('NumberTitle', 'off', 'Name', ... 'Aggregation and Defuzzification for Input = (4, 6)'); plot (x_axis, fuzzy_output(:, 1), "b;Aggregated Fuzzy Output;", ... 'LineWidth', 2); hold on; crisp_output = evalmf(x_axis, output(1), 'constant'); y_label = ["r;Crisp Output = " num2str(output(1)) "%;"]; plot (x_axis, crisp_output, y_label, 'LineWidth', 2); ylim ([-0.1, 1.1]); xlabel ('Tip', 'FontWeight', 'bold'); grid; hold; ## Show the rules in symbolic format. puts ("\nMamdani Tip Calculator Rules:\n\n"); showrule (fis, 1:columns(fis.rule), 'symbolic'); %!test %! fis = readfis ('mamdani_tip_calculator.fis'); %! food_service = [1 1; 5 5; 10 10; 4 6; 6 4; 7 4]; %! tip = evalfis (food_service, fis, 1001); %! expected_result = ... %! [10.0000 1.1000 %! 15.0000 1.1500 %! 20.0000 1.2000 %! 15.0000 1.1500 %! 15.0000 1.1500 %! 16.4708 1.1647]; %! assert(tip, expected_result, 1e-4); fuzzy-logic-toolkit-0.6.1/inst/newfis.m000066400000000000000000000131631466512601400201220ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{a} =} newfis (@var{fis_name}) ## @deftypefnx {Function File} {@var{a} =} newfis (@var{fis_name}, @var{fis_type}) ## @deftypefnx {Function File} {@var{a} =} newfis (@var{fis_name}, @var{fis_type}, @var{and_method}) ## @deftypefnx {Function File} {@var{a} =} newfis (@var{fis_name}, @var{fis_type}, @var{and_method}, @var{or_method}) ## @deftypefnx {Function File} {@var{a} =} newfis (@var{fis_name}, @var{fis_type}, @var{and_method}, @var{or_method}, @var{imp_method}) ## @deftypefnx {Function File} {@var{a} =} newfis (@var{fis_name}, @var{fis_type}, @var{and_method}, @var{or_method}, @var{imp_method}, @var{agg_method}) ## @deftypefnx {Function File} {@var{a} =} newfis (@var{fis_name}, @var{fis_type}, @var{and_method}, @var{or_method}, @var{imp_method}, @var{agg_method}, @var{defuzz_method}) ## @deftypefnx {Function File} {@var{a} =} newfis (@var{fis_name}, @var{fis_type}, @var{and_method}, @var{or_method}, @var{imp_method}, @var{agg_method}, @var{defuzz_method}, @var{fis_version}) ## ## Create and return a new FIS structure using the argument values provided. ## Only the first argument is required. If fewer than eight arguments are given, ## then some or all of the following default values will be used: ## ## @multitable @columnfractions .30 .30 ## @headitem Argument @tab Default Value ## @item @var{fis_type} ## @tab 'mamdani' ## @item @var{and_method} ## @tab 'min' ## @item @var{or_method} ## @tab 'max' ## @item @var{imp_method} ## @tab 'min' ## @item @var{agg_method} ## @tab 'max' ## @item @var{defuzz_method} ## @tab 'centroid' ## @item @var{fis_version} ## @tab 1.0 ## @end multitable ## @sp 1 ## @seealso{addmf, addrule, addvar, setfis} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: newfis.m ## Last-Modified: 12 Jun 2024 function fis = newfis (fis_name, fis_type = 'mamdani', ... and_method = 'min', or_method = 'max', ... imp_method = 'min', agg_method = 'max', ... defuzz_method = 'centroid', fis_version = 1.0) ## If the caller did not supply the between 1 and 8 argument values, ## or if any of the argument values were not strings, print an error ## message and halt. if (!(nargin >= 1 && nargin <= 8)) error ("newfis requires between 1 and 8 arguments\n"); elseif (!(is_string (fis_name) && is_string (fis_type) && ... is_string (and_method) && is_string (or_method) && ... is_string (imp_method) && is_string (agg_method) && ... is_string (defuzz_method) && isfloat (fis_version))) error ("incorrect argument type in newfis argument list\n"); endif ## Create and return the new FIS structure. fis = struct ('name', fis_name, ... 'type', fis_type, ... 'version', fis_version, ... 'andMethod', and_method, ... 'orMethod', or_method, ... 'impMethod', imp_method, ... 'aggMethod', agg_method, ... 'defuzzMethod', defuzz_method, ... 'input', [], ... 'output', [], ... 'rule', []); endfunction %!shared fis %! fis = newfis ('Heart-Disease-Risk', 'sugeno', ... %! 'min', 'max', 'min', 'max', 'wtaver'); %!assert(fis.name == 'Heart-Disease-Risk'); %!assert(fis.type == 'sugeno'); %!assert(fis.andMethod == 'min'); %!assert(fis.orMethod == 'max'); %!assert(fis.impMethod == 'min'); %!assert(fis.aggMethod == 'max'); %!assert(fis.defuzzMethod == 'wtaver'); ## Test input validation %!error %! newfis() %!error %! newfis(1, 2, 3, 4, 5, 6, 7, 8, 9) %!error %! newfis(1, 'str', 'str', 'str', 'str', 'str', 'str', 8) %!error %! newfis(1, 'str', 'str', 'str', 'str', 'str', 'str', 8) %!error %! newfis('str', 2, 'str', 'str', 'str', 'str', 'str', 8) %!error %! newfis('str', 'str', 3, 'str', 'str', 'str', 'str', 8) %!error %! newfis('str', 'str', 'str', 4, 'str', 'str', 'str', 8) %!error %! newfis('str', 'str', 'str', 'str', 5, 'str', 'str', 8) %!error %! newfis('str', 'str', 'str', 'str', 'str', 6, 'str', 8) %!error %! newfis('str', 'str', 'str', 'str', 'str', 'str', 7, 8) %!error %! newfis('str', 'str', 'str', 'str', 'str', 'str', 'str', 'str') fuzzy-logic-toolkit-0.6.1/inst/partition_coeff.m000066400000000000000000000063641466512601400220070ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{vpc} =} partition_coeff (@var{soft_partition}) ## ## Return the partition coefficient for a given soft partition. ## ## The argument to partition_coeff is: ## @itemize @w ## @item ## @var{soft_partition}: the membership degree of each input data point in each cluster ## @end itemize ## ## The return value is: ## @itemize @w ## @item ## @var{vpc}: the partition coefficient for the given soft partition ## @end itemize ## ## To run demonstration code that uses this function, type "@t{demo fcm}" ## or "@t{demo gustafson_kessel}" (without the quotation marks) at the ## Octave prompt. ## ## For more information about the @var{soft_partition} matrix, please see the ## documentation for function fcm. ## ## @seealso{fcm, gustafson_kessel, partition_entropy, xie_beni_index} ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit partition coefficient cluster ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: partition_coeff.m ## Last-Modified: 13 Jun 2024 ##---------------------------------------------------------------------- ## Note: This function is an implementation of Equation 13.9 (corrected ## -- the equation in the book omits the exponent 2) in ## Fuzzy Logic: Intelligence, Control and Information, by J. Yen ## and R. Langari, Prentice Hall, 1999, page 384 (International ## Edition). ##---------------------------------------------------------------------- function vpc = partition_coeff (soft_partition) ## If partition_coeff was called with an incorrect number of ## arguments, or the argument does not have the correct type, ## print an error message and halt. if (nargin != 1) error ("partition_coeff requires 1 argument\n"); elseif (!(is_real_matrix (soft_partition) && (min (min (soft_partition)) >= 0) && (max (max (soft_partition)) <= 1))) error ("partition_coeff's argument must be a matrix of reals 0.0-1.0\n"); endif ## Compute and return the partition coefficient. soft_part_sqr = soft_partition .* soft_partition; vpc = (sum (sum (soft_part_sqr))) / columns (soft_partition); endfunction ## Test input validation %!error %! partition_coeff() %!error %! partition_coeff(1, 2) %!error %! partition_coeff([-1 2]) fuzzy-logic-toolkit-0.6.1/inst/partition_entropy.m000066400000000000000000000072331466512601400224210ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{vpe} =} partition_entropy (@var{soft_partition}, @var{a}) ## ## Return the partition entropy for a given soft partition. ## ## The arguments to partition_entropy are: ## @itemize @w ## @item ## @var{soft_partition}: the membership degree of each input data point in each cluster ## @item ## @var{a}: the log base to use in the calculation; must be a real number a > 1 ## @end itemize ## ## The return value is: ## @itemize @w ## @item ## @var{vpe}: the partition entropy for the given soft partition ## @end itemize ## ## To run demonstration code that uses this function, type "@t{demo fcm}" ## or "@t{demo gustafson_kessel}" (without the quotation marks) at the ## Octave prompt. ## ## For more information about the @var{soft_partition} matrix, please see the ## For more information about the @var{soft_partition} matrix, please see the ## documentation for function fcm. ## ## @seealso{fcm, gustafson_kessel, partition_coeff, xie_beni_index} ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit partition entropy cluster ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: partition_entropy.m ## Last-Modified: 13 Jun 2024 ##---------------------------------------------------------------------- ## Note: This function is an implementation of Equation 13.10 in ## Fuzzy Logic: Intelligence, Control and Information, by J. Yen ## and R. Langari, Prentice Hall, 1999, page 384 (International ## Edition). ##---------------------------------------------------------------------- function vpe = partition_entropy (soft_partition, a) ## If partition_entropy was called with an incorrect number of ## arguments, or the argument does not have the correct type, print an ## error message and halt. if (nargin != 2) error ("partition_entropy requires 2 arguments\n"); elseif (!(is_real_matrix (soft_partition) && (min (min (soft_partition)) >= 0) && (max (max (soft_partition)) <= 1))) error ("partition_entropy's 1st arg must be a matrix of reals 0.0-1.0\n"); elseif (!(is_real (a) && a > 1)) error ("partition_entropy's 2nd arg must be a real greater than 1\n"); endif ## Compute and return the partition entropy. n = columns (soft_partition); Mu = soft_partition; log_a_Mu = log (Mu) / log (a); vpe = -(sum (sum (Mu .* log_a_Mu))) / n; endfunction ## Test input validation %!error %! partition_entropy() %!error %! partition_entropy(1) %!error %! partition_entropy(1, 2, 3) %!error %! partition_entropy([1 2], 2) %!error %! partition_entropy([1 1], -2) fuzzy-logic-toolkit-0.6.1/inst/pimf.m000066400000000000000000000144141466512601400175620ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} pimf (@var{x}, @var{params}) ## @deftypefnx {Function File} {@var{y} =} pimf (@var{[x1 x2 ... xn]}, @var{[a b c d]}) ## ## For a given domain @var{x} and parameters @var{params} (or @var{[a b c d]}), ## return the corresponding @var{y} values for the pi-shaped membership ## function. ## ## The argument @var{x} must be a real number or a non-empty vector of real ## numbers, and @var{a}, @var{b}, @var{c}, and @var{d} must be real numbers, ## with @var{a} < @var{b} <= @var{c} < @var{d}. This membership function ## satisfies: ## ## @verbatim ## 0 if x <= a ## 2 * ((x - a)/(b - a))^2 if a < x <= (a + b)/2 ## 1 - 2 * ((x - b)/(b - a))^2 if (a + b)/2 < x < b ## f(x) = 1 if b <= x <= c ## 1 - 2 * ((x - c)/(d - c))^2 if c < x <= (c + d)/2 ## 2 * ((x - d)/(d - c))^2 if (c + d)/2 < x < d ## 0 if x >= d ## @end verbatim ## ## which always returns values in the range [0, 1]. ## ## To run the demonstration code, type "@t{demo pimf}" (without the quotation ## marks) at the Octave prompt. ## ## @seealso{dsigmf, gauss2mf, gaussmf, gbellmf, psigmf, sigmf, smf, trapmf, trimf, zmf} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy membership pi-shaped pi ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: pimf.m ## Last-Modified: 13 Jun 2024 function y = pimf (x, params) ## If the caller did not supply 2 argument values with the correct ## types, print an error message and halt. if ((nargin != 2)) error ("pimf requires 2 arguments\n"); elseif (!is_domain (x)) error ("pimf's first argument must be a valid domain\n"); elseif (!are_mf_params ('pimf', params)) error ("pimf's second argument must be a parameter vector\n"); endif ## Calculate and return the y values of the membership function on the ## domain x. a = params(1); b = params(2); c = params(3); d = params(4); a_b_ave = (a + b) / 2; b_minus_a = b - a; c_d_ave = (c + d) / 2; d_minus_c = d - c; y_val = @(x_val) pimf_val (x_val, a, b, c, d, a_b_ave, b_minus_a, ... c_d_ave, d_minus_c); y = arrayfun (y_val, x); endfunction ##---------------------------------------------------------------------- ## Usage: y = pimf_val (x_val, a, b, c, d, a_b_ave, b_minus_a, c_d_ave, ## d_minus_c) ## ## pimf_val returns one value of the S-shaped membership function, which ## satisfies: ## 0 if x <= a ## 2 * ((x - a)/(b - a))^2 if a < x <= (a + b)/2 ## 1 - 2 * ((x - b)/(b - a))^2 if (a + b)/2 < x < b ## f(x) = 1 if b <= x <= c ## 1 - 2 * ((x - c)/(d - c))^2 if c < x <= (c + d)/2 ## 2 * ((x - d)/(d - c))^2 if (c + d)/2 < x < d ## 0 if x >= d ## ## pimf_val is a private function, called only by pimf. Because pimf_val ## is not intended for general use -- and because the parameters a, b, ## c, and d are checked for errors in the function pimf (defined above), ## the parameters are not checked for errors again here. ##---------------------------------------------------------------------- function y_val = pimf_val (x_val, a, b, c, d, a_b_ave, b_minus_a, ... c_d_ave, d_minus_c) ## Calculate and return a single y value of the pi-shaped membership ## function for the given x value and parameters specified by the ## arguments. if (x_val <= a) y_val = 0; elseif (x_val <= a_b_ave) y_val = 2 * ((x_val - a)/b_minus_a)^2; elseif (x_val < b) y_val = 1 - 2 * ((x_val - b) / b_minus_a)^2; elseif (x_val <= c) y_val = 1; elseif (x_val <= c_d_ave) y_val = 1 - 2 * ((x_val - c) / d_minus_c)^2; elseif (x_val < d) y_val = 2 * ((x_val - d) / d_minus_c)^2; else y_val = 0; endif endfunction %!demo %! x = 0:255; %! params = [70 80 100 140]; %! y1 = pimf(x, params); %! params = [50 75 105 175]; %! y2 = pimf(x, params); %! params = [30 70 110 200]; %! y3 = pimf(x, params); %! figure('NumberTitle', 'off', 'Name', 'pimf demo'); %! plot(x, y1, 'r;params = [70 80 100 140];', 'LineWidth', 2) %! hold on; %! plot(x, y2, 'b;params = [50 75 105 175];', 'LineWidth', 2) %! hold on; %! plot(x, y3, 'g;params = [30 70 110 200];', 'LineWidth', 2) %! ylim([-0.1 1.1]); %! xlabel('Crisp Input Value', 'FontWeight', 'bold'); %! ylabel('Degree of Membership', 'FontWeight', 'bold'); %! grid; %!test %! x = 0:25:250; %! params = [50 75 105 175]; %! y = [0 0 0 1 1 0.8367 0.2551 0 0 0 0]; %! z = pimf(x, params); %! assert(z, y, 1e-4); ## Test input validation %!error %! pimf() %!error %! pimf(1) %!error %! pimf(1, 2, 3) %!error %! pimf([1 0], 2) %!error %! pimf(1, 2) %!error %! pimf(0:100, []) %!error %! pimf(0:100, [30]) %!error %! pimf(0:100, [2 3]) %!error %! pimf(0:100, [90 80 30]) %!error %! pimf(0:100, 'abc') fuzzy-logic-toolkit-0.6.1/inst/plotmf.m000066400000000000000000000161351466512601400201320ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {} plotmf (@var{fis}, @var{in_or_out}, @var{var_index}) ## @deftypefnx {Function File} {} plotmf (@var{fis}, @var{in_or_out}, @var{var_index}, @var{y_lower_limit}) ## @deftypefnx {Function File} {} plotmf (@var{fis}, @var{in_or_out}, @var{var_index}, @var{y_lower_limit}, @var{y_upper_limit}) ## ## Plot the membership functions defined for the specified FIS input or output ## variable on a single set of axes. Fuzzy output membership functions are ## represented by the [0, 1]-valued fuzzy functions, and constant output ## membership functions are represented by unit-valued singleton spikes. ## Linear output membership functions, however, are represented by ## two-dimensional lines y = ax + c, regardless of how many dimensions the ## linear function is defined to have. In effect, all of the other dimensions ## of the linear function are set to 0. ## ## If both constant and linear membership functions are used for a single FIS ## output, then two sets of axes are used: one for the constant membership ## functions, and another for the linear membership functions. To plot both ## constant and linear membership functions together, or to plot constant ## membership functions as horizontal lines instead of unit-valued spikes, ## represent the constant membership functions using 'linear' functions, with ## 0 for all except the last parameter, and with the desired constant value as ## the last parameter. ## ## The types/values of the arguments are expected to be: ## ## @multitable @columnfractions .30 .65 ## @headitem Argument @tab Expected Type or Value ## @item @var{fis} ## @tab an FIS structure ## @item @var{in_or_out} ## @tab either 'input' or 'output' (case-insensitive) ## @item @var{var_index} ## @tab an FIS input or output variable index ## @item @var{y_lower_limit} ## @tab a real scalar (default value = -0.1) ## @item @var{y_upper_limit} ## @tab a real scalar (default value = 1.1) ## @end multitable ## @sp 1 ## Six examples that use plotmf are: ## @itemize @bullet ## @item ## cubic_approx_demo.m ## @item ## heart_disease_demo_1.m ## @item ## heart_disease_demo_2.m ## @item ## investment_portfolio_demo.m ## @item ## linear_tip_demo.m ## @item ## mamdani_tip_demo.m ## @item ## sugeno_tip_demo.m ## @end itemize ## ## @seealso{gensurf} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy membership plot ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: plotmf.m ## Last-Modified: 12 Jun 2024 function plotmf (fis, in_or_out, var_index, ... y_lower_limit = -0.1, y_upper_limit = 1.1) ## If the caller did not supply 3 argument values with the correct ## types, print an error message and halt. if ((nargin < 3) || (nargin > 5)) error ("plotmf requires 3 - 5 arguments\n"); elseif (!is_fis (fis)) error ("plotmf's first argument must be an FIS structure\n"); elseif (!(is_string (in_or_out) && ... ismember (tolower (in_or_out), {'input', 'output'}))) error ("plotmf's second argument must be 'input' or 'output'\n"); elseif (!is_var_index (fis, in_or_out, var_index)) error ("plotmf's third argument must be a variable index\n"); elseif (!(is_real (y_lower_limit) && is_real (y_upper_limit))) error ("plotmf's 4th and 5th arguments must be real scalars\n"); endif ## Select specified variable and construct the window title. if (strcmpi (in_or_out, 'input')) var = fis.input(var_index); window_title = [' Input ' num2str(var_index) ' Term Set']; else var = fis.output(var_index); window_title = [' Output ' num2str(var_index) ' Term Set']; endif ## Plot the membership functions for the specified variable. ## Cycle through the five colors: red, blue, green, magenta, cyan. ## Display the membership function names in a legend. colors = ["r" "b" "g" "m" "c"]; x = linspace (var.range(1), var.range(2), 1001); num_mfs = columns (var.mf); ## Define vectors to keep track of linear and non-linear mfs. linear_mfs = zeros (1, num_mfs); for i = 1 : num_mfs if (strcmp ('linear', var.mf(i).type)) linear_mfs(i) = 1; endif endfor fuzzy_and_constant_mfs = 1 - linear_mfs; ## Plot the fuzzy or constant membership functions together on a set ## of axes. if (sum (fuzzy_and_constant_mfs)) figure ('NumberTitle', 'off', 'Name', window_title); ## Plot the mfs. for i = 1 : num_mfs if (fuzzy_and_constant_mfs(i)) y = evalmf_private (x, var.mf(i).params, var.mf(i).type); y_label = [colors(mod(i-1,5)+1) ";" var.mf(i).name ";"]; plot (x, y, y_label, 'LineWidth', 2); hold on; endif endfor ## Adjust the y-axis, label both axes, and display a dotted grid. ylim ([y_lower_limit y_upper_limit]); xlabel (var.name, 'FontWeight', 'bold'); ylabel ('Degree of Membership', 'FontWeight', 'bold'); grid; hold; endif ## Plot the linear membership functions together on a separate set ## of axes. if (sum (linear_mfs)) figure ('NumberTitle', 'off', 'Name', window_title); ## Plot the mfs. for i = 1 : num_mfs if (linear_mfs(i)) y = evalmf_private (x, var.mf(i).params, var.mf(i).type); y_label = [colors(mod(i-1,5)+1) ";" var.mf(i).name ";"]; plot (x, y, y_label, 'LineWidth', 2); hold on; endif endfor ## Adjust the y-axis, label both axes, and display a dotted grid. ylim ([y_lower_limit y_upper_limit]); xlabel ('X', 'FontWeight', 'bold'); ylabel (var.name, 'FontWeight', 'bold'); grid; hold; endif endfunction %!shared fis %! fis = readfis ('cubic_approximator.fis'); ## Test input validation %!error %! plotmf() %!error %! plotmf(1) %!error %! plotmf(1, 2) %!error %! plotmf(1, 2, 3, 4, 5, 6) %!error %! plotmf(1, 2, 3) %!error %! plotmf(fis, 2, 3) %!error %! plotmf(fis, 'input', 3) %!error %! plotmf(fis, 'input', 1, 2j) %!error %! plotmf(fis, 'input', 1, 0, 2j) fuzzy-logic-toolkit-0.6.1/inst/private/000077500000000000000000000000001466512601400201175ustar00rootroot00000000000000fuzzy-logic-toolkit-0.6.1/inst/private/aggregate_output_mamdani.m000066400000000000000000000073541466512601400253420ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{fuzzy_output} =} aggregate_output_mamdani (@var{fis}, @var{rule_output}) ## ## Given the: ## @itemize @bullet ## @item @var{fis.aggMethod:} ## the aggregation method for the given @var{fis} ## @item @var{rule_output:} ## a matrix of the fuzzy output for each (rule, FIS output) pair ## @end itemize ## ## Return: ## @itemize @bullet ## @item @var{fuzzy_output:} ## a matrix of the aggregated output for each FIS output variable ## @end itemize ## ## @var{rule_output} is a @var{num_points} x (Q * M) matrix, where ## @var{num_points} is the number of points over which the fuzzy ## values are evaluated, Q is the number of rules and M is the number ## of FIS output variables. Each column of @var{rule_output} gives ## the y-values of the fuzzy output for a single (rule, FIS output) ## pair: ## ## @verbatim ## Q cols Q cols Q cols ## --------------- --------------- --------------- ## out_1 ... out_1 out_2 ... out_2 ... out_M ... out_M ## 1 [[ ] ## 2 [ ] ## ... [ ] ## num_points [ ]] ## @end verbatim ## ## The return value @var{fuzzy_output} is a @var{num_points} x M matrix. Each ## column of @var{fuzzy_output} gives the y-values of the fuzzy output for a ## single FIS output variable, aggregated over all rules: ## ## @verbatim ## out_1 out_2 ... out_M ## 1 [[ ] ## 2 [ ] ## ... [ ] ## num_points [ ]] ## @end verbatim ## ## Because aggregate_output_mamdani is called only by the private ## function evalfis_private, it does no error checking of the argument values. ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: aggregate_output_mamdani.m ## Last-Modified: 26 Jul 2024 function fuzzy_output = aggregate_output_mamdani (fis, rule_output) num_rules = columns (fis.rule); ## num_rules == Q (above) num_outputs = columns (fis.output); ## num_outputs == L num_points = rows (rule_output); ## Initialize output matrix to prevent inefficient resizing. fuzzy_output = zeros (num_points, num_outputs); ## Compute the ith fuzzy output values, then store the values in the ## ith column of the fuzzy_output matrix. for i = 1 : num_outputs indiv_fuzzy_out = ... rule_output(:, (i - 1) * num_rules + 1 : i * num_rules); agg_fuzzy_out = (str2func (fis.aggMethod) (indiv_fuzzy_out'))'; fuzzy_output(:, i) = agg_fuzzy_out; endfor endfunction fuzzy-logic-toolkit-0.6.1/inst/private/aggregate_output_sugeno.m000066400000000000000000000132111466512601400252210ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{fuzzy_output} =} aggregate_output_sugeno (@var{fis}, @var{rule_output}) ## ## Given the: ## @itemize @bullet ## @item @var{fis.aggMethod:} ## the aggregation method for the given @var{fis} ## @item @var{rule_output:} ## a matrix of the singleton output of each (rule, FIS output) pair ## @end itemize ## ## Return: ## @itemize @bullet ## @item @var{fuzzy_output:} ## a vector of structures containing the aggregated output for each FIS output ## @end itemize ## ## @var{rule_output} is a 2 x (Q * M) matrix, where Q is the number of rules ## and M is the number of FIS output variables. Each column of @var{rule_output} ## gives the (location, height) pair of the singleton output for one ## (rule, FIS output) pair: ## ## @verbatim ## Q cols Q cols Q cols ## --------------- --------------- --------------- ## out_1 ... out_1 out_2 ... out_2 ... out_M ... out_M ## location [[ ] ## height [ ]] ## @end verbatim ## ## The return value @var{fuzzy_output} is a vector of M structures, ## each of which has an index i and a matrix of singletons that form the ## aggregated output for the ith FIS output variable. ## For each FIS output variable, the matrix of singletons is a 2 x L matrix ## where L is the number of distinct singleton locations in the fuzzy output ## for that FIS output variable. The first row gives the (distinct) locations, ## and the second gives the (non-zero) heights: ## ## @verbatim ## singleton_1 singleton_2 ... singleton_L ## location [[ ] ## height [ ]] ## @end verbatim ## ## Because aggregate_output_sugeno is called only by the private ## function evalfis_private, it does no error checking of the argument values. ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: aggregate_output_sugeno.m ## Last-Modified: 26 Jul 2024 ##---------------------------------------------------------------------- function fuzzy_output = aggregate_output_sugeno (fis, rule_output) fuzzy_output = []; num_outputs = columns (fis.output); num_rules = columns (fis.rule); ## For each FIS output, aggregate the slice of the rule_output matrix, ## then store the result as a structure in fuzzy_output. for i = 1 : num_outputs unagg_output = rule_output(:, (i-1)*num_rules+1 : i*num_rules); aggregated_output = aggregate_fis_output (fis.aggMethod, ... unagg_output); next_agg_output = struct ('index', i, ... 'aggregated_output', aggregated_output); if (i == 1) fuzzy_output = next_agg_output; else fuzzy_output = [fuzzy_output, next_agg_output]; endif endfor endfunction ##---------------------------------------------------------------------- ## Function: aggregate_fis_output ## Purpose: Aggregate the multiple singletons for one FIS output. ##---------------------------------------------------------------------- function mult_singletons = aggregate_fis_output (fis_aggmethod, ... rule_output) ## Initialize output matrix (multiple_singletons). mult_singletons = sortrows (rule_output', 1); ## If adjacent rows represent singletons at the same location, then ## combine them using the FIS aggregation method. for i = 1 : rows (mult_singletons) - 1 if (mult_singletons(i, 1) == mult_singletons(i+1, 1)) switch (fis_aggmethod) case 'sum' mult_singletons(i + 1, 2) = mult_singletons(i, 2) + ... mult_singletons(i + 1, 2); otherwise mult_singletons(i + 1, 2) = str2func (fis_aggmethod) ... (mult_singletons(i, 2), ... mult_singletons(i + 1, 2)); endswitch mult_singletons(i, 2) = 0; endif endfor ## Return the transpose of the matrix after removing 0-height ## singletons. mult_singletons = (remove_null_rows (mult_singletons))'; endfunction ##---------------------------------------------------------------------- ## Function: remove_null_rows ## Purpose: Return the argument without the rows with a 0 in the ## second column. ##---------------------------------------------------------------------- function y = remove_null_rows (x) y = []; for i = 1 : rows (x) if (x(i, 2) != 0) if (isequal (y, [])) y = x(i, :); else y = [y; x(i, :)]; endif endif endfor endfunction fuzzy-logic-toolkit-0.6.1/inst/private/are_bounds.m000066400000000000000000000030601466512601400224150ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} are_bounds (@var{x}) ## @deftypefnx {Function File} {@var{y} =} are_bounds (@var{[x1 x2]}) ## ## Return 1 if @var{x} is a vector of 2 real numbers @var{[x1 x2]}, ## with @var{x1} <= @var{x2}, and return 0 otherwise. ## ## are_bounds is a private function that localizes the test for validity of ## bounds imposed on FIS input/output domains. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: are_bounds.m ## Last-Modified: 20 Aug 2012 function y = are_bounds (x) y = isvector (x) && isreal (x) && (length (x) == 2) && (x(1) <= x(2)); endfunction fuzzy-logic-toolkit-0.6.1/inst/private/are_input_indices.m000066400000000000000000000032121466512601400237570ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} are_input_indices (@var{x}, @var{fis}) ## ## Return 1 if @var{x} is a valid input index or a vector of two valid input ## indices for the given FIS structure, and return 0 otherwise. The FIS ## structure @var{fis} is assumed to be valid. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: are_input_indices.m ## Last-Modified: 20 Aug 2012 function y = are_input_indices (x, fis) if (!(isreal (x) && isvector (x) && (length (x) <= 2))) y = 0; else y = 1; num_inputs = columns (fis.input); for next_x = x if (!(is_pos_int (next_x) && next_x <= num_inputs)) y = 0; endif endfor endif endfunction fuzzy-logic-toolkit-0.6.1/inst/private/are_mf_params.m000066400000000000000000000146411466512601400230770ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} are_mf_params (@var{type}, @var{params}) ## ## Return 0 if @var{type} is a built-in membership function and @var{params} ## are not valid parameters for that type, and return 1 otherwise. ## ## are_mf_params is a private function that localizes the test for validity of ## membership function parameters. Note that for a custom membership function, ## this function always returns 1. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: are_mf_params.m ## Last-Modified: 20 Aug 2012 function y = are_mf_params (type, params) switch (type) case 'constant' y = real_vector (params); case 'dsigmf' y = four_reals (params); case 'gauss2mf' y = four_reals (params); case 'gaussmf' y = two_reals (params); case 'gbellmf' y = gbellmf_params (params); case 'linear' y = real_vector (params); case 'pimf' y = pimf_params (params); case 'psigmf' y = four_reals (params); case 'sigmf' y = two_reals (params); case 'smf' y = smf_params (params); case 'trapmf' y = trapmf_params (params); case 'trimf' y = trimf_params (params); case 'zmf' y = zmf_params (params); otherwise y = 1; endswitch endfunction ##---------------------------------------------------------------------- ## Usage: y = real_vector (params) ## ## Return 1 if params is a vector of real numbers, and ## return 0 otherwise. ##---------------------------------------------------------------------- function y = real_vector (params) y = isvector (params) && isreal (params); endfunction ##---------------------------------------------------------------------- ## Usage: y = two_reals (params) ## ## Return 1 if params is a vector of 2 real numbers, and ## return 0 otherwise. ##---------------------------------------------------------------------- function y = two_reals (params) y = isvector (params) && isreal (params) && (length (params) == 2); endfunction ##---------------------------------------------------------------------- ## Usage: y = three_reals (params) ## ## Return 1 if params is a vector of 3 real numbers, and ## return 0 otherwise. ##---------------------------------------------------------------------- function y = three_reals (params) y = isvector (params) && isreal (params) && (length (params) == 3); endfunction ##---------------------------------------------------------------------- ## Usage: y = four_reals (params) ## ## Return 1 if params is a vector of 4 real numbers, and ## return 0 otherwise. ##---------------------------------------------------------------------- function y = four_reals (params) y = isvector (params) && isreal (params) && (length (params) == 4); endfunction ##---------------------------------------------------------------------- ## Usage: y = gbellmf_params (params) ## y = gbellmf_params ([a b c]) ## ## Return 1 if params is a vector of 3 real numbers, [a b c], with ## a != 0 and integral-valued b, and return 0 otherwise. ##---------------------------------------------------------------------- function y = gbellmf_params (params) y = three_reals (params) && (params(1) != 0) && is_int (params(2)); endfunction ##---------------------------------------------------------------------- ## Usage: y = pimf_params (params) ## y = pimf_params ([a b c d]) ## ## Return 1 if params is a vector of 4 real numbers, [a b c d], with ## a < b <= c < d, and return 0 otherwise. ##---------------------------------------------------------------------- function y = pimf_params (params) y = four_reals (params) && ... (params(1) < params(2)) && ... (params(2) <= params(3)) && ... (params(3) < params(4)); endfunction ##---------------------------------------------------------------------- ## Usage: y = smf_params (params) ## y = smf_params ([a b]) ## ## Return 1 if params is a vector of 2 real numbers, [a b], with a < b, ## and return 0 otherwise. ##---------------------------------------------------------------------- function y = smf_params (params) y = two_reals (params) && (params(1) < params(2)); endfunction ##---------------------------------------------------------------------- ## Usage: y = trapmf_params (params) ## y = trapmf_params ([a b c d]) ## ## Return 1 if params is a vector of 4 real numbers, [a b c d], with ## a < b <= c < d, and return 0 otherwise. ##---------------------------------------------------------------------- function y = trapmf_params (params) y = four_reals (params) && ... (params(1) < params(2)) && ... (params(2) <= params(3)) && ... (params(3) < params(4)); endfunction ##---------------------------------------------------------------------- ## Usage: y = trimf_params (params) ## y = trimf_params ([a b c]) ## ## Return 1 if params is a vector of 3 real numbers, [a b c], with ## a < b < c, and return 0 otherwise. ##---------------------------------------------------------------------- function y = trimf_params (params) y = three_reals (params) && ... (params(1) < params(2)) && ... (params(2) < params(3)); endfunction ##---------------------------------------------------------------------- ## Usage: y = zmf_params (params) ## y = zmf_params ([a b]) ## ## Return 1 if params is a vector of 2 real numbers, [a b], with a < b, ## and return 0 otherwise. ##---------------------------------------------------------------------- function y = zmf_params (params) y = two_reals (params) && (params(1) < params(2)); endfunction fuzzy-logic-toolkit-0.6.1/inst/private/compute_cluster_convergence.m000066400000000000000000000031741466512601400260750ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{convergence_criterion} =} compute_cluster_convergence (@var{V}, @var{V_previous}) ## ## Compute the sum of the changes in position (using the Euclidean ## distance) of the cluster prototypes. ## ## @seealso{fcm, gustafson_kessel, init_cluster_prototypes, update_cluster_membership, update_cluster_prototypes, compute_cluster_obj_fcn} ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy partition clustering ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: compute_cluster_convergence.m ## Last-Modified: 2 Sep 2012 function convergence_criterion = ... compute_cluster_convergence (V, V_previous) V_delta = V - V_previous; convergence_criterion = sum (sqrt (sum (V_delta .* V_delta)')); endfunction fuzzy-logic-toolkit-0.6.1/inst/private/compute_cluster_obj_fcn.m000066400000000000000000000035661466512601400252040ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{obj_fcn} =} compute_cluster_obj_fcn (@var{Mu_m}, @var{sqr_dist}) ## ## Compute the objective function for the current iteration. ## ## @seealso{fcm, gustafson_kessel, init_cluster_prototypes, update_cluster_membership, update_cluster_prototypes, compute_cluster_convergence} ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy partition clustering ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: compute_cluster_obj_fcn.m ## Last-Modified: 2 Sep 2012 ##---------------------------------------------------------------------- ## Note: This function is an implementation of Equation 13.3 in ## Fuzzy Logic: Intelligence, Control and Information, by ## J. Yen and R. Langari, Prentice Hall, 1999, page 379 ## (International Edition). ##---------------------------------------------------------------------- function obj_fcn = compute_cluster_obj_fcn (Mu_m, sqr_dist) obj_fcn = sum (sum (Mu_m .* sqr_dist)); endfunction fuzzy-logic-toolkit-0.6.1/inst/private/defuzzify_output_mamdani.m000066400000000000000000000056161466512601400254320ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{output} =} defuzzify_output_mamdani (@var{fis}, @var{fuzzy_output}) ## ## Given the: ## @itemize @bullet ## @item @var{fis.defuzzMethod:} ## the defuzzification method for the given @var{fis} ## @item @var{fuzzy_output:} ## a matrix of the aggregated output for each FIS output variable ## @end itemize ## ## Return: ## @itemize @bullet ## @item @var{output:} ## a vector of crisp output values ## @end itemize ## ## @var{fuzzy_output} is a @var{num_points} x M matrix, where @var{num_points} ## is the number of points over which fuzzy values are evaluated and M is the ## number of FIS output variables. Each ## column of @var{fuzzy_output} gives the y-values of the fuzzy output for a ## single FIS output variable, aggregated over all rules: ## ## @verbatim ## out_1 out_2 ... out_M ## 1 [[ ] ## 2 [ ] ## ... [ ] ## num_points [ ]] ## @end verbatim ## ## The crisp @var{output} values are computed from the corresponding fuzzy ## values using the FIS defuzzification method. The @var{output} ## vector has the form: ## ## @verbatim ## output: [output_1 output_2 ... output_M] ## @end verbatim ## ## Because defuzzify_output_mamdani is called only by the private ## function evalfis_private, it does no error checking of the argument values. ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: defuzzify_output_mamdani.m ## Last-Modified: 26 Jul 2024 function output = defuzzify_output_mamdani (fis, fuzzy_output) num_outputs = columns (fis.output); ## num_outputs == L (above) num_points = rows (fuzzy_output); output = zeros (1, num_outputs); for i = 1 : num_outputs range = fis.output(i).range; x = linspace (range(1), range(2), num_points); y = (fuzzy_output(:, i))'; output(i) = defuzz (x, y, fis.defuzzMethod); endfor endfunction fuzzy-logic-toolkit-0.6.1/inst/private/defuzzify_output_sugeno.m000066400000000000000000000057611466512601400253250ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{output} =} defuzzify_output_sugeno (@var{fis}, @var{aggregated_output}) ## ## Given the: ## @itemize @bullet ## @item @var{fis.defuzzMethod:} ## the defuzzification method for the given @var{fis} ## @item @var{aggregated_output:} ## a vector of structures containing the aggregated output for each FIS output variable ## @end itemize ## ## Return: ## @itemize @bullet ## @item @var{output:} ## a vector of crisp output values ## @end itemize ## ## The @var{aggregated_output} is a vector of M structures, where M is the ## number of FIS output variables. Each structure contains an index i and a ## matrix of singletons that form the aggregated output for the ith FIS output. ## For each FIS output variable, the matrix of singletons is a 2 x L matrix ## where L is the number of distinct singleton locations in the fuzzy output ## for that FIS output variable. The first row gives the (distinct) locations, ## and the second gives the (non-zero) heights: ## ## @verbatim ## singleton_1 singleton_2 ... singleton_L ## location [[ ] ## height [ ]] ## @end verbatim ## ## The crisp @var{output} values are computed from the corresponding fuzzy ## values using the FIS defuzzification method. The @var{output} ## vector has the form: ## ## @verbatim ## output: [output_1 output_2 ... output_M] ## @end verbatim ## ## Because defuzzify_output_sugeno is called only by the private ## function evalfis_private, it does no error checking of the argument values. ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: defuzzify_output_sugeno.m ## Last-Modified: 26 Jul 2024 function output = defuzzify_output_sugeno (fis, aggregated_output) num_outputs = columns (fis.output); output = zeros (1, num_outputs); for i = 1 : num_outputs next_agg_output = aggregated_output(i).aggregated_output; x = next_agg_output(1, :); y = next_agg_output(2, :); output(i) = defuzz (x, y, fis.defuzzMethod); endfor endfunction fuzzy-logic-toolkit-0.6.1/inst/private/eval_firing_strength.m000066400000000000000000000120331466512601400244770ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{firing_strength} =} eval_firing_strength (@var{fis}, @var{rule_input}) ## ## Return the firing strength for each FIS rule given a matrix of matching ## degrees for each (rule, rule_input) pair. ## ## The second argument (@var{rule_input}) gives the fuzzified input values to ## the FIS rules as a Q x N matrix: ## ## @verbatim ## in_1 in_2 ... in_N ## rule_1 [[mu_11 mu_12 ... mu_1N] ## rule_2 [mu_21 mu_22 ... mu_2N] ## [ ... ] ## rule_Q [mu_Q1 mu_Q2 ... mu_QN]] ## @end verbatim ## ## where Q is the number of rules and N is the number of FIS input variables. ## ## For i = 1 .. Q, the fuzzy antecedent, connection, and weight for rule i ## are given by: ## @itemize @bullet ## @item ## @var{fis.rule(i).antecedent} ## @item ## @var{fis.rule(i).connection} ## @item ## @var{fis.rule(i).weight} ## @end itemize ## ## The output is a row vector of length Q. ## ## Because eval_firing_strength is called only by the private function ## evalfis_private, it does no error checking of the argument values. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: eval_firing_strength.m ## Last-Modified: 13 Jun 2024 function firing_strength = eval_firing_strength (fis, rule_input) num_rules = columns (fis.rule); ## num_rules == Q (above) num_inputs = columns (fis.input); ## num_inputs == N ## Initialize output matrix to prevent inefficient resizing. firing_strength = zeros (1, num_rules); ## For each rule ## 1. Apply connection to find matching degree of the antecedent. ## 2. Multiply by weight of the rule to find degree of the rule. for i = 1 : num_rules rule = fis.rule(i); ## Collect mu values for all input variables in the antecedent. antecedent_mus = []; for j = 1 : num_inputs if (rule.antecedent(j) != 0) mu = rule_input(i, j); antecedent_mus = [antecedent_mus mu]; endif endfor ## Compute matching degree of the rule. if (rule.connection == 1) connect = fis.andMethod; else connect = fis.orMethod; endif switch (connect) case 'min' firing_strength(i) = rule.weight * ... min (antecedent_mus); case 'max' firing_strength(i) = rule.weight * ... max (antecedent_mus); case 'prod' firing_strength(i) = rule.weight * ... prod (antecedent_mus); case 'sum' firing_strength(i) = rule.weight * ... sum (antecedent_mus); case 'algebraic_product' firing_strength(i) = rule.weight * ... prod (antecedent_mus); case 'algebraic_sum' firing_strength(i) = rule.weight * ... algebraic_sum (antecedent_mus); case 'bounded_difference' firing_strength(i) = rule.weight * ... bounded_difference (antecedent_mus); case 'bounded_sum' firing_strength(i) = rule.weight * ... bounded_sum (antecedent_mus); case 'einstein_product' firing_strength(i) = rule.weight * ... einstein_product (antecedent_mus); case 'einstein_sum' firing_strength(i) = rule.weight * ... einstein_sum (antecedent_mus); case 'hamacher_product' firing_strength(i) = rule.weight * ... hamacher_product (antecedent_mus); case 'hamacher_sum' firing_strength(i) = rule.weight * ... hamacher_sum (antecedent_mus); case 'drastic_product' firing_strength(i) = rule.weight * ... drastic_product (antecedent_mus); case 'drastic_sum' firing_strength(i) = rule.weight * ... drastic_sum (antecedent_mus); otherwise firing_strength(i) = rule.weight * ... str2func (connect) (antecedent_mus); endswitch endfor endfunction fuzzy-logic-toolkit-0.6.1/inst/private/eval_rules_mamdani.m000066400000000000000000000112501466512601400241230ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{rule_output} =} eval_rules_mamdani (@var{fis}, @var{firing_strength}, @var{num_points}) ## ## Return the fuzzy output for each (rule, FIS output) pair ## for a Mamdani-type FIS (an FIS that does not have constant or linear ## output membership functions). ## ## The firing strength of each rule is given by a row vector of length Q, where ## Q is the number of rules in the FIS: ## ## @verbatim ## rule_1 rule_2 ... rule_Q ## [firing_strength(1) firing_strength(2) ... firing_strength(Q)] ## @end verbatim ## ## The implication method and fuzzy consequent for each rule are given by: ## ## @verbatim ## fis.impMethod ## fis.rule(i).consequent for i = 1..Q ## @end verbatim ## ## The return value, @var{rule_output}, is a @var{num_points} x (Q * M) ## matrix, where Q is the number of rules and M is the number of FIS output ## variables. Each column of this matrix gives the y-values of the fuzzy ## output for a single (rule, FIS output) pair. ## ## @verbatim ## Q cols Q cols Q cols ## --------------- --------------- --------------- ## out_1 ... out_1 out_2 ... out_2 ... out_M ... out_M ## 1 [[ ] ## 2 [ ] ## ... [ ] ## num_points [ ]] ## @end verbatim ## ## Because eval_rules_mamdani is called only by the private function ## evalfis_private, it does no error checking of the argument values. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: eval_rules_mamdani.m ## Last-Modified: 13 Jun 2024 function rule_output = eval_rules_mamdani (fis, firing_strength, ... num_points) num_rules = columns (fis.rule); ## num_rules == Q (above) num_outputs = columns (fis.output); ## num_outputs == L ## Initialize output matrix to prevent inefficient resizing. rule_output = zeros (num_points, num_rules*num_outputs); ## Compute the fuzzy output for each (rule, output) pair: ## 1. Apply the FIS implication method to find the fuzzy outputs ## for the current (rule, output) pair. ## 2. Store the result as a column in the rule_output matrix. for i = 1 : num_rules rule = fis.rule(i); rule_matching_degree = firing_strength(i); if (rule_matching_degree != 0) for j = 1 : num_outputs ## Compute the fuzzy output for this (rule, output) pair. [mf_index hedge not_flag] = ... get_mf_index_and_hedge (rule.consequent(j)); if (mf_index != 0) ## First, get the fuzzy output, adjusting for the hedge and ## not_flag, but not for the rule matching degree. range = fis.output(j).range; mf = fis.output(j).mf(mf_index); x = linspace (range(1), range(2), num_points); fuzzy_out = evalmf (x, mf.params, mf.type, hedge, not_flag); ## Adjust the fuzzy output for the rule matching degree. switch (fis.impMethod) case 'min' fuzzy_out = min (rule_matching_degree, fuzzy_out); case 'prod' fuzzy_out *= rule_matching_degree; otherwise fuzzy_out = str2func (fis.impMethod) ... (rule_matching_degree, fuzzy_out); endswitch ## Store result in column of rule_output corresponding ## to the (rule, output) pair. rule_output(:, (j - 1) * num_rules + i) = fuzzy_out'; endif endfor endif endfor endfunction fuzzy-logic-toolkit-0.6.1/inst/private/eval_rules_sugeno.m000066400000000000000000000120061466512601400240150ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{rule_output} =} eval_rules_sugeno (@var{fis}, @var{firing_strength}, @var{user_input}) ## ## Return the fuzzy output for each (rule, FIS output) pair for a ## Sugeno-type FIS (an FIS that has only constant and linear output ## membership functions). ## ## The firing strength of each rule is given by a row vector of length Q, where ## Q is the number of rules in the FIS: ## @example ## @group ## rule_1 rule_2 ... rule_Q ## [firing_strength(1) firing_strength(2) ... firing_strength(Q)] ## @end group ## @end example ## ## The consequent for each rule is given by: ## @example ## fis.rule(i).consequent for i = 1..Q ## @end example ## ## The return value of the function is a 2 x (Q * M) matrix, where ## M is the number of FIS output variables. ## Each column of this matrix gives the (location, height) pair of the ## singleton output for a single (rule, FIS output) pair. ## ## @example ## @group ## Q cols Q cols Q cols ## --------------- --------------- --------------- ## out_1 ... out_1 out_2 ... out_2 ... out_M ... out_M ## location [[ ] ## height [ ]] ## @end group ## @end example ## ## Note that for Sugeno FISs, the hedge and not flag are handled by ## adjusting the height of the singletons for each (rule, output) pair. ## ## Because eval_rules_sugeno is called only by the private function ## evalfis_private, it does no error checking of the argument values. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: eval_rules_sugeno.m ## Last-Modified: 10 Jun 2024 function rule_output = eval_rules_sugeno (fis, firing_strength, ... user_input) num_rules = columns (fis.rule); ## num_rules == Q (above) num_outputs = columns (fis.output); ## num_outputs == L ## Initialize output matrix to prevent inefficient resizing. rule_output = zeros (2, num_rules * num_outputs); ## Compute the (location, height) of the singleton output by each ## (rule, output) pair: ## 1. The height is given by the firing strength of the rule, and ## by the hedge and the not flag for the (rule, output) pair. ## 2. If the consequent membership function is constant, then the ## membership function's parameter gives the location of the ## singleton. If the consequent membership function is linear, ## then the location is the inner product of the the membership ## function's parameters and the vector formed by appending a 1 ## to the user input vector. for i = 1 : num_rules rule = fis.rule(i); rule_firing_strength = firing_strength(i); if (rule_firing_strength != 0) for j = 1 : num_outputs ## Compute the singleton height for this (rule, output) pair. ## Note that for Sugeno FISs, the hedge and not flag are handled ## by adjusting the height of the singletons for each ## (rule, output) pair. [mf_index hedge not_flag] = ... get_mf_index_and_hedge (rule.consequent(j)); height = rule_firing_strength; if (hedge != 0) height = height ^ (1 / hedge); endif if (not_flag) height = 1 - height; endif ## Compute the singleton location for this (rule, output) pair. if (mf_index != 0) mf = fis.output(j).mf(mf_index); switch (mf.type) case 'constant' location = mf.params; case 'linear' location = mf.params * [user_input 1]'; otherwise location = str2func (mf.type) (mf.params, user_input); endswitch ## Store result in column of rule_output corresponding ## to the (rule, output) pair. rule_output(1, (j - 1) * num_rules + i) = location; rule_output(2, (j - 1) * num_rules + i) = height; endif endfor endif endfor endfunction fuzzy-logic-toolkit-0.6.1/inst/private/evalfis_private.m000066400000000000000000000057741466512601400234750ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{output} =} evalfis_private (@var{input}, @var{fis}) ## @deftypefnx {Function File} {@var{output} =} evalfis_private (@var{input}, @var{fis}, @var{num_points}) ## @deftypefnx {Function File} {[@var{output}, @var{rule_input}, @var{rule_output}, @var{fuzzy_output}] =} evalfis_private (@var{input}, @var{fis}) ## @deftypefnx {Function File} {[@var{output}, @var{rule_input}, @var{rule_output}, @var{fuzzy_output}] =} evalfis_private (@var{input}, @var{fis}, @var{num_points}) ## ## This function localizes the FIS evaluation common to the public functions ## evalfis and gensurf. All of the arguments to evalfis_private are assumed to ## be valid (limiting the inefficiency of the tests to the calling function). ## ## For more information, see the comments at the top of evalfis.m and gensurf.m. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: evalfis_private.m ## Last-Modified: 20 Aug 2012 function [output, rule_input, rule_output, fuzzy_output] = ... evalfis_private (user_input, fis, num_points = 101) ## Initialize output matrix (to prevent repeated resizing). output = zeros (rows (user_input), columns (fis.output)); ## Process one set of inputs at a time. For each row of crisp input ## values in the input matrix, add a row of crisp output values to the ## output matrix. for i = 1 : rows (user_input) rule_input = fuzzify_input (fis, user_input(i, :)); firing_strength = eval_firing_strength (fis, rule_input); if (strcmp (fis.type, 'mamdani')) rule_output = eval_rules_mamdani (fis, firing_strength, ... num_points); fuzzy_output = aggregate_output_mamdani (fis, rule_output); output(i, :) = defuzzify_output_mamdani (fis, fuzzy_output); else rule_output = eval_rules_sugeno (fis, firing_strength, ... user_input(i, :)); fuzzy_output = aggregate_output_sugeno (fis, rule_output); output(i, :) = defuzzify_output_sugeno (fis, fuzzy_output); endif endfor endfunction fuzzy-logic-toolkit-0.6.1/inst/private/evalmf_private.m000066400000000000000000000102561466512601400233050ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} evalmf_private (@var{x}, @var{param}, @var{mf_type}) ## @deftypefnx {Function File} {@var{y} =} evalmf_private (@var{x}, @var{param}, @var{mf_type}, @var{hedge}) ## @deftypefnx {Function File} {@var{y} =} evalmf_private (@var{x}, @var{param}, @var{mf_type}, @var{hedge}, @var{not_flag}) ## @deftypefnx {Function File} {@var{y} =} evalmf_private (@var{[x1 x2 ... xn]}, @var{[param1 ... ]}, '<@var{mf_type}>') ## @deftypefnx {Function File} {@var{y} =} evalmf_private (@var{[x1 x2 ... xn]}, @var{[param1 ... ]}, '<@var{mf_type}>', @var{hedge}) ## @deftypefnx {Function File} {@var{y} =} evalmf_private (@var{[x1 x2 ... xn]}, @var{[param1 ... ]}, '<@var{mf_type}>', @var{hedge}, @var{not_flag}) ## ## This function localizes the membership function evaluation without the ## parameter tests. It is called by evalmf and plotmf. For more information, ## see the comment at the top of evalmf.m. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy membership-function evaluate ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: evalmf_private.m ## Last-Modified: 3 Sep 2012 function y = evalmf_private (x, params, mf_type, hedge = 0, ... not_flag = false) ## Calculate and return the y values of the membership function on ## the domain x. First, get the value of the membership function ## without correcting for the hedge and not_flag. Then, for non-linear ## functions, adjust the function values for non-zero hedge and ## not_flag. switch (mf_type) case 'constant' y = eval_constant (x, params); if (not_flag) y = 1 - y; endif case 'linear' y = eval_linear (x, params); otherwise y = str2func (mf_type) (x, params); if (hedge != 0) y = y .^ hedge; endif if (not_flag) y = 1 - y; endif endswitch endfunction ##---------------------------------------------------------------------- ## Function: eval_constant ## Purpose: Return the y-values corresponding to the x-values in ## the domain for the constant function specified by the ## parameter c. ##---------------------------------------------------------------------- function y = eval_constant (x, c) y = zeros (length (x)); delta = x(2) - x(1); y_val = @(x_val) ((abs (c - x_val) < delta) * 1); y = arrayfun (y_val, x); endfunction ##---------------------------------------------------------------------- ## Function: eval_linear ## Purpose: For the parameters [a ... c]), return the y-values ## corresponding to the linear function y = a*x + c, where x ## takes on the the x-values in the domain. The remaining ## coefficients in the parameter list are not used -- this ## creates a two-dimensional intersection of the linear output ## membership function suitable for display together with ## other membership functions, but does not fully represent ## the output membership function. ##---------------------------------------------------------------------- function y = eval_linear (x, params) if (length (params) == 1) a = 0; c = params; else a = params(1); c = params(length (params)); endif y = zeros (length (x)); y_val = @(x_val) (a * x_val + c); y = arrayfun (y_val, x); endfunction fuzzy-logic-toolkit-0.6.1/inst/private/fuzzify_input.m000066400000000000000000000061671466512601400232340ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{rule_input} =} fuzzify_input (@var{fis}, @var{user_input}) ## ## Return the matching degree for each (rule, input value) pair. ## For an FIS that has Q rules and N FIS input variables, the return value ## will be a Q x N matrix. ## ## The crisp input values are given by a row vector: ## ## @verbatim ## user_input: [input_1 input_2 ... input_N] ## @end verbatim ## ## The rule antecedents are stored in the FIS structure as row vectors: ## ## @verbatim ## rule 1 antecedent: [in_11 in_12 ... in_1N] ## rule 2 antecedent: [in_21 in_22 ... in_2N] ## ... ... ## rule Q antecedent: [in_Q1 in_Q2 ... in_QN] ## @end verbatim ## ## Finally, the output of the function gives the matching degree ## for each (rule, input value) pair as an Q x N matrix: ## ## @verbatim ## in_1 in_2 ... in_N ## rule_1 [[mu_11 mu_12 ... mu_1N] ## rule_2 [mu_21 mu_22 ... mu_2N] ## [ ... ] ## rule_Q [mu_Q1 mu_Q2 ... mu_QN]] ## @end verbatim ## ## Because fuzzify_input is called only by the private function ## evalfis_private, it does no error checking of the argument values. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: fuzzify_input.m ## Last-Modified: 31 Aug 2024 function rule_input = fuzzify_input (fis, user_input) num_rules = columns (fis.rule); ## num_rules == Q (above) num_inputs = columns (fis.input); ## num_inputs == N rule_input = zeros (num_rules, num_inputs); ## to prevent resizing ## For each rule i and each input j, compute the value of mu ## in the result. for i = 1 : num_rules antecedent = fis.rule(i).antecedent; for j = 1 : num_inputs mu = 0; crisp_x = user_input(j); ## Get the value of mu (with adjustment for the hedge ## and not_flag). [mf_index hedge not_flag] = ... get_mf_index_and_hedge (antecedent(j)); if (mf_index != 0) mf = fis.input(j).mf(mf_index); mu = evalmf (crisp_x, mf.params, mf.type, hedge, not_flag); endif ## Store the fuzzified input in rule_input. rule_input(i, j) = mu; endfor endfor endfunction fuzzy-logic-toolkit-0.6.1/inst/private/get_mf_index_and_hedge.m000066400000000000000000000050231466512601400247030ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{[mf_index hedge not_flag]} =} get_mf_index_and_hedge (@var{mf_index_and_hedge}) ## ## Return the membership function index, hedge, and "not" flag ## indicated by the argument. ## ## The membership function index, @var{mf_index}, is the positive whole number ## portion of the argument. The @var{hedge} is the fractional part of the ## argument, rounded to 2 digits and multiplied by 10. The @var{not_flag}, ## a Boolean, is true iff the argument is negative. ## ## Because get_mf_index_and_hedge is a private function, it does no error ## checking of its argument. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: get_mf_index_and_hedge.m ## Last-Modified: 10 Jun 2024 function [mf_index hedge not_flag] = ... get_mf_index_and_hedge (mf_index_and_hedge) ## Set flag to handle "not", indicated by a minus sign in the ## antecedent. if (mf_index_and_hedge < 0) not_flag = true; mf_index_and_hedge = -mf_index_and_hedge; else not_flag = false; endif ## The membership function index is the positive whole number portion ## of an element in the antecedent. mf_index = fix (mf_index_and_hedge); ## For custom hedges and the four built-in hedges "somewhat", "very", ## "extremely", and "very very", return the power to which the ## membership value should be raised. The hedges are indicated by the ## fractional part of the corresponding rule_matrix entry (rounded to ## 2 digits). if (mf_index != 0) hedge = round (100 * (mf_index_and_hedge - mf_index)) / 10; else hedge = 0; endif endfunction fuzzy-logic-toolkit-0.6.1/inst/private/init_cluster_prototypes.m000066400000000000000000000033751466512601400253210ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{V} =} init_cluster_prototypes (@var{X}, @var{k}) ## ## Initialize k cluster centers to random locations in the ranges ## given by the min/max values of each feature of the dataset. ## ## @seealso{fcm, gustafson_kessel, update_cluster_membership, update_cluster_prototypes, compute_cluster_obj_fcn, compute_cluster_convergence} ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy partition clustering ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: init_cluster_prototypes.m ## Last-Modified: 2 Sep 2012 function V = init_cluster_prototypes (X, k) num_features = columns (X); min_feature_value = min (X); max_feature_value = max (X); V = rand (k, num_features); for i = 1 : num_features V(:, i) = (max_feature_value(i) - min_feature_value(i)) * ... V(:, i) + min_feature_value(i); endfor endfunction fuzzy-logic-toolkit-0.6.1/inst/private/is_builtin_language.m000066400000000000000000000037771466512601400243170ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_builtin_language (@var{x}) ## ## Return true if @var{x} is one of the strings representing the ## built-in languages, and return false otherwise. The comparison is ## case-insensitive. ## ## is_builtin_language is a private function that localizes the test ## for languages handled by showrule. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_builtin_language.m ## Last-Modified: 31 Aug 2024 function y = is_builtin_language (x) y = ischar (x) && isvector (x) && ... ismember (tolower (x), {'english', ... 'chinese', 'mandarin', 'pinyin', ... 'russian', 'russkij', 'pycckii', ... 'french', 'francais', ... 'spanish', 'espanol', ... 'german', 'deutsch'}); endfunction %!assert(is_builtin_language(6), false) %!assert(is_builtin_language('english'), true) %!assert(is_builtin_language('francais'), true) %!assert(is_builtin_language(''), false) fuzzy-logic-toolkit-0.6.1/inst/private/is_domain.m000066400000000000000000000034471466512601400222470ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_domain (@var{x}) ## @deftypefnx {Function File} {@var{y} =} is_domain (@var{[x1 x2 ... xn]}) ## ## Return true if @var{x} is a real number of a vector of strictly increasing real ## numbers, and return false otherwise. ## ## is_domain is a private function that localizes the test for validity of FIS ## input variable domains. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_domain.m ## Last-Modified: 31 Aug 2024 function y = is_domain (x) y = 1; if (!(isvector (x) && isreal (x))) y = 0; elseif (length(x) > 1) for i = 1 : length (x) - 1 if (x(i) >= x(i + 1)) y = 0; endif endfor endif endfunction %!assert(is_domain(6), 1) %!assert(is_domain([1 2]), 1) %!assert(is_domain([2 1]), 0) %!assert(is_domain([]), 0) %!assert(is_domain('hello'), 0) fuzzy-logic-toolkit-0.6.1/inst/private/is_fis.m000066400000000000000000000045171466512601400215600ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_fis (@var{x}) ## ## Return true if the argument @var{x} is a valid FIS (Fuzzy Inference System) ## structure, and return false otherwise. ## ## is_fis is a private function that localizes the test for valid FIS structs. ## For efficiency, is_fis only determines if the argument @var{x} is a structure ## with the expected fields, and that these fields have the expected types. ## ## Examples: ## @verbatim ## fis = newfis('FIS'); ## is_fis(fis) ==> true ## @end verbatim ## ## @verbatim ## x = pi; ## is_fis(x) ==> false ## @end verbatim ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_fis.m ## Last-Modified: 31 Aug 2024 function y = is_fis (x) y = isstruct (x) && ... isfield (x, 'name') && is_string (x.name) && ... isfield (x, 'type') && is_string (x.type) && ... isfield (x, 'andMethod') && is_string (x.andMethod) && ... isfield (x, 'orMethod') && is_string (x.orMethod) && ... isfield (x, 'impMethod') && is_string (x.impMethod) && ... isfield (x, 'aggMethod') && is_string (x.aggMethod) && ... isfield (x, 'defuzzMethod') && is_string (x.defuzzMethod) && ... isfield (x, 'input') && is_io_vector (x.input) && ... isfield (x, 'output') && is_io_vector (x.output) && ... isfield (x, 'rule') && is_rule_vector (x.rule); endfunction fuzzy-logic-toolkit-0.6.1/inst/private/is_format.m000066400000000000000000000030231466512601400222560ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_format (@var{x}) ## ## Return true if @var{x} is one of the strings 'verbose', 'symbolic', and ## 'indexed', and return false otherwise. The comparison is case-insensitive. ## ## is_format is a private function that localizes the test for valid fis rule ## input/output formats. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_format.m ## Last-Modified: 10 Jun 2024 function y = is_format (x) y = ischar (x) && isvector (x) && ... ismember (tolower (x), {'verbose', 'symbolic', 'indexed'}); endfunction fuzzy-logic-toolkit-0.6.1/inst/private/is_grid_spec.m000066400000000000000000000027211466512601400227310ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_grid_spec (@var{x}) ## ## Return 1 if @var{x} is an integer or vector of two integers, each >= 2, ## and return 0 otherwise. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_grid_spec.m ## Last-Modified: 20 Aug 2012 function y = is_grid_spec (x, fis) if (!(isvector (x) && (length (x) <= 2))) y = 0; else y = 1; for next_x = x if (!(is_int (next_x) && next_x >= 2)) y = 0; endif endfor endif endfunction fuzzy-logic-toolkit-0.6.1/inst/private/is_input_matrix.m000066400000000000000000000033561466512601400235220ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_input_matrix (@var{x}, @var{fis}) ## ## Return 1 if @var{x} is a valid matrix of input values for the given FIS ## structure, and return 0 otherwise. The FIS structure @var{fis} is assumed ## to be valid. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_input_matrix.m ## Last-Modified: 20 Aug 2012 function y = is_input_matrix (x, fis) if (!(ismatrix (x) && isreal (x) && ... (columns (x) == columns (fis.input)))) y = 0; else y = 1; for j = 1 : columns (x) range = fis.input(j).range; for i = 1 : rows(x) if (!(isscalar (x(i, j)) && ... x(i,j) >= range(1) && ... x(i,j) <= range(2))) y = 0; endif endfor endfor endif endfunction fuzzy-logic-toolkit-0.6.1/inst/private/is_int.m000066400000000000000000000036311466512601400215650ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_int (@var{x}) ## ## Return true if @var{x} is an integer-valued real scalar, and ## return false otherwise. ## ## is_int is a private function that localizes the test for integers. ## In Octave, integer constants such as 1 are not represented by ints ## internally: isinteger(1) returns 0. ## ## Examples: ## @verbatim ## is_int(6) ==> true ## is_int(6.2) ==> false ## is_int(ones(2)) ==> false ## is_int(6 + 0i) ==> true ## is_int(0) ==> true ## @end verbatim ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_int.m ## Last-Modified: 31 Aug 2024 function y = is_int (x) y = isscalar (x) && isreal (x) && (fix (x) == x); endfunction ## Tests corresponding to examples in the comment at the top of this file. %!assert(is_int(6), true) %!assert(is_int(6.2), false) %!assert(is_int(ones(2)), false) %!assert(is_int(6 + 0i), true) %!assert(is_int(0), true) fuzzy-logic-toolkit-0.6.1/inst/private/is_io_struct.m000066400000000000000000000034051466512601400230050ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_io_struct (@var{x}) ## ## Return true if the argument @var{x} is a valid input or output structure for an ## FIS (Fuzzy Inference System), and return false otherwise. ## ## is_io_struct is a private function that localizes the test for valid input ## and output structs. For efficiency, is_io_struct only determines if the ## argument @var{x} is a structure with the expected fields, and that these ## fields have the expected types. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_io_struct.m ## Last-Modified: 10 Jun 2024 function y = is_io_struct (x) y = isstruct (x) && ... isfield (x, 'name') && is_string (x.name) && ... isfield (x, 'range') && are_bounds (x.range) && ... isfield (x, 'mf') && is_mf_vector (x.mf); endfunction fuzzy-logic-toolkit-0.6.1/inst/private/is_io_vector.m000066400000000000000000000031301466512601400227560ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_io_vector (@var{x}) ## ## Return 1 if @var{x} is a vector of FIS input/output variable structures, ## and return 0 otherwise. ## ## is_io_vector is a private function that localizes the test for valid FIS ## structure members 'input' and 'output'. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_io_vector.m ## Last-Modified: 20 Aug 2012 function y = is_io_vector (x) y = 1; if (isequal(x, [])) y = 1; elseif (!isvector(x)) y = 0; else y = 1; for i = 1 : length (x) if (!is_io_struct (x(i))) y = 0; endif endfor endif endfunction fuzzy-logic-toolkit-0.6.1/inst/private/is_mf_index.m000066400000000000000000000040341466512601400225620ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_mf_index (@var{fis}, @var{in_or_out}, @var{var_index}, @var{mf_index}) ## ## If @var{in_or_out} == 'input', return true if @var{mf_index} is a valid ## membership function index for the input variable with index @var{var_index}, ## and return false otherwise. ## ## If @var{in_or_out} == 'output', return true if @var{mf_index} is a valid ## membership function index for the output variable with index @var{var_index}, ## and return false otherwise. ## ## is_mf_index is a private function that localizes the test for valid FIS ## membership function indices. The arguments @var{fis}, @var{in_or_out}, and ## @var{var_index} are assumed to be valid. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_mf_index.m ## Last-Modified: 10 Jun 2024 function y = is_mf_index (fis, in_or_out, var_index, mf_index) y = is_int (mf_index) && (mf_index >= 1); if (strcmp (in_or_out, 'input')) y = y && (mf_index <= length (fis.input(var_index).mf)); else y = y && (mf_index <= length (fis.output(var_index).mf)); endif endfunction fuzzy-logic-toolkit-0.6.1/inst/private/is_mf_struct.m000066400000000000000000000033061466512601400230000ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_mf_struct (@var{x}) ## ## Return true if the argument @var{x} is a valid FIS (Fuzzy Inference System) ## membership function structure, and return false otherwise. ## ## is_mf_struct is a private function that localizes the test for valid FIS ## membership function structs. For efficiency, is_mf_struct only determines if ## the argument @var{x} is a structure with the expected fields, but the types ## of the fields are not verified. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_mf_struct.m ## Last-Modified: 10 Jun 2024 function y = is_mf_struct (x) y = isstruct (x) && ... isfield (x, 'name') && ... isfield (x, 'type') && ... isfield (x, 'params'); endfunction fuzzy-logic-toolkit-0.6.1/inst/private/is_mf_vector.m000066400000000000000000000030541466512601400227560ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_mf_vector (@var{x}) ## ## Return 1 if @var{x} is a vector of FIS membership function structures, and ## return 0 otherwise. ## ## is_mf_vector is a private function that localizes the test for validity. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_mf_vector.m ## Last-Modified: 20 Aug 2012 function y = is_mf_vector (x) y = 1; if (isequal(x, [])) y = 1; elseif (!isvector (x)) y = 0; else y = 1; for i = 1 : length (x) if (!is_mf_struct (x(i))) y = 0; endif endfor endif endfunction fuzzy-logic-toolkit-0.6.1/inst/private/is_output_index.m000066400000000000000000000026421466512601400235230ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_output_index (@var{x}, @var{fis}) ## ## Return true if @var{x} is a valid output index for the given FIS structure, ## and return false otherwise. The FIS structure @var{fis} is assumed to be ## valid. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_output_index.m ## Last-Modified: 10 Jun 2024 function y = is_output_index (x, fis) y = is_pos_int (x) && (x <= columns (fis.output)); endfunction fuzzy-logic-toolkit-0.6.1/inst/private/is_pos_int.m000066400000000000000000000030301466512601400224370ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_pos_int (@var{x}) ## ## Return true if @var{x} is a positive integer-valued real scalar, and return ## false otherwise. ## ## Examples: ## @verbatim ## is_pos_int(6) ==> true ## is_pos_int(6.2) ==> false ## is_pos_int(ones(2)) ==> false ## is_pos_int(6 + 0i) ==> true ## is_pos_int(0) ==> false ## @end verbatim ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_pos_int.m ## Last-Modified: 31 Aug 2024 function y = is_pos_int (x) y = is_int (x) && (x > 0); endfunction fuzzy-logic-toolkit-0.6.1/inst/private/is_real.m000066400000000000000000000037641466512601400217250ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_real (@var{x}) ## ## Return true if @var{x} is an real scalar, and return false otherwise. ## ## is_real is a private function that localizes the test for real scalars. ## ## Examples: ## @verbatim ## is_real(6) ==> true ## is_real(6.2) ==> true ## is_real(ones(2)) ==> false ## is_real(6 + 0i) ==> true ## is_real(6 + i) ==> false ## is_real([0]) ==> true ## is_real([0 0]) ==> false ## is_real('h') ==> false ## @end verbatim ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_real.m ## Last-Modified: 31 Aug 2024 function y = is_real (x) y = isnumeric(x) && isscalar (x) && isreal (x); endfunction ## Tests corresponding to examples in the comment at the top of this file. %!assert(is_real(6), true) %!assert(is_real(6.2), true) %!assert(is_real(ones(2)), false) %!assert(is_real(6 + 0i), true) %!assert(is_real(6 + i), false) %!assert(is_real([0]), true) %!assert(is_real([0 0]), false) %!assert(is_real('h'), false) fuzzy-logic-toolkit-0.6.1/inst/private/is_real_matrix.m000066400000000000000000000040511466512601400232770ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_real_matrix (@var{x}) ## ## Return 1 if @var{x} is a non-empty matrix of real or integer-valued scalars, ## and return 0 otherwise. ## ## Examples: ## @verbatim ## is_real_matrix(6) ==> 1 ## is_real_matrix([]) ==> 1 ## is_real_matrix([1 2; 3 4]) ==> 1 ## is_real_matrix([1 2 3]) ==> 1 ## is_real_matrix([i 2 3]) ==> 0 ## is_real_matrix("hello") ==> 0 ## @end verbatim ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_real_matrix.m ## Last-Modified: 31 Aug 2024 function y = is_real_matrix (x) if (!ismatrix (x)) y = 0; else y = 1; for i = 1 : numel (x) if (!(isnumeric (x(i)) && isscalar (x(i)) && isreal (x(i)))) y = 0; endif endfor endif endfunction ## Tests corresponding to examples in the comment at the top of this file. %!assert(is_real_matrix(6), 1) %!assert(is_real_matrix([]), 1) %!assert(is_real_matrix([1 2; 3 4]), 1) %!assert(is_real_matrix([1 2 3]), 1) %!assert(is_real_matrix([i 2 3]), 0) %!assert(is_real_matrix("hello"), 0) fuzzy-logic-toolkit-0.6.1/inst/private/is_ref_input.m000066400000000000000000000034771466512601400227760ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_ref_input (@var{x}, @var{fis}, @var{graphed_inputs}) ## ## Return 1 if @var{x} is a vector of constants for the FIS structure inputs ## that are not included in the list of inputs, and return 0 otherwise. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_ref_input.m ## Last-Modified: 20 Aug 2012 function y = is_ref_input (x, fis, graphed_inputs) y = 1; num_fis_inputs = columns (fis.input); num_graphed_inputs = length (graphed_inputs); if (!(is_row_vector (x) && (length (x) == num_fis_inputs))) y = 0; else for i = 1 : num_fis_inputs range = fis.input(i).range; if (!(isreal (x(i)) && isscalar (x(i)))) y = 0; elseif (!ismember (i, graphed_inputs) && ... (x(i) < range(1) || x(i) > range(2))) y = 0; endif endfor endif endfunction fuzzy-logic-toolkit-0.6.1/inst/private/is_row_vector.m000066400000000000000000000032331466512601400231620ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_row_vector (@var{x}) ## ## Return true if @var{x} is a non-empty row vector, and return ## false otherwise. ## ## Examples: ## @verbatim ## is_row_vector([]) ==> false ## is_row_vector([1 2 3]) ==> true ## is_row_vector([1; 2; 3]) ==> false ## @end verbatim ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_row_vector.m ## Last-Modified: 31 Aug 2024 function y = is_row_vector (x) y = isvector (x) && (rows (x) == 1); endfunction ## Tests corresponding to examples in the comment at the top of this file. %!assert(is_row_vector([]), false) %!assert(is_row_vector([1 2 3]), true) %!assert(is_row_vector([1; 2; 3]), false) fuzzy-logic-toolkit-0.6.1/inst/private/is_rule_index_list.m000066400000000000000000000036271466512601400241710ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_rule_index_list (@var{x}, @var{max_index}) ## ## Return 1 if @var{x} is a valid rule index or a vector of valid rule indices, ## and return 0 otherwise. ## ## Examples: ## @verbatim ## is_rule_index_list(2, 5) ==> 1 ## is_rule_index_list([1 2], 5) ==> 1 ## is_rule_index_list([1, 2], 5) ==> 1 ## is_rule_index_list([1; 2], 5) ==> 1 ## is_rule_index_list(0, 0) ==> 0 ## is_rule_index_list([4 5], 2) ==> 0 ## is_rule_index_list([], 2) ==> 0 ## @end verbatim ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_rule_index_list.m ## Last-Modified: 31 Aug 2024 function y = is_rule_index_list (x, max_index) if (is_pos_int (x)) y = (x <= max_index); elseif (!isvector (x)) y = 0; else y = 1; for i = 1 : length (x) if (!(is_pos_int (x(i)) && (x(i) <= max_index))) y = 0; endif endfor endif endfunction fuzzy-logic-toolkit-0.6.1/inst/private/is_rule_struct.m000066400000000000000000000033451466512601400233500ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_rule_struct (@var{x}) ## ## Return true if the argument @var{x} is a valid FIS (Fuzzy Inference System) ## rule structure, and return false otherwise. ## ## is_rule_struct is a private function that localizes the test for valid FIS ## rule structs. For efficiency, is_rule_struct only determines if the argument ## @var{x} is a structure with the expected fields, but the types of the fields ## are not verified. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_rule_struct.m ## Last-Modified: 10 Jun 2024 function y = is_rule_struct (x) y = isstruct (x) && ... isfield (x, 'antecedent') && ... isfield (x, 'consequent') && ... isfield (x, 'weight') && ... isfield (x, 'connection'); endfunction fuzzy-logic-toolkit-0.6.1/inst/private/is_rule_vector.m000066400000000000000000000030611466512601400233210ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_rule_vector (@var{x}) ## ## Return 1 if @var{x} is a vector of FIS rule structures, and return 0 ## otherwise. ## ## is_rule_vector is a private function that localizes the test for valid FIS ## 'rule' members. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_rule_vector.m ## Last-Modified: 20 Aug 2012 function y = is_rule_vector (x) if (isequal(x, [])) y = 1; elseif (!isvector (x)) y = 0; else y = 1; for i = 1 : length (x) if (!is_rule_struct (x(i))) y = 0; endif endfor endif endfunction fuzzy-logic-toolkit-0.6.1/inst/private/is_string.m000066400000000000000000000031521466512601400222770ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_string (@var{x}) ## ## Return true if @var{x} is a character vector, and return false otherwise. ## ## is_string is a private function that localizes the test for valid Octave ## strings, which may need to be changed in the future. Octave 3.2.4 implements ## strings as character vectors. In subsequent versions of Octave, the internal ## implementation of strings may change, or a built-in Octave test 'isstring' ## may be implemented. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_string.m ## Last-Modified: 10 Jun 2024 function y = is_string (x) y = ischar (x) && isvector (x); endfunction fuzzy-logic-toolkit-0.6.1/inst/private/is_var_index.m000066400000000000000000000036501466512601400227530ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} is_var_index (@var{fis}, @var{in_or_out}, @var{var_index}) ## ## If @var{in_or_out} == 'input', return true if @var{var_index} is a valid input ## variable index for the given FIS structure, and return false otherwise. ## ## If @var{in_or_out} == 'output', return true if @var{var_index} is a valid output ## variable index for the given FIS structure, and return false otherwise. ## ## is_var_index is a private function that localizes the test for valid FIS ## input and output variable indices. The arguments @var{fis} and ## @var{in_or_out} are assumed to be valid. ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private parameter-test ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: is_var_index.m ## Last-Modified: 10 Jun 2024 function y = is_var_index (fis, in_or_out, var_index) y = is_int (var_index) && (var_index >= 1); if (strcmp (in_or_out, 'input')) y = y && (var_index <= length (fis.input)); else y = y && (var_index <= length (fis.output)); endif endfunction fuzzy-logic-toolkit-0.6.1/inst/private/square_distance_matrix.m000066400000000000000000000064101466512601400250340ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{sqr_dist} =} square_distance_matrix (@var{X}, @var{V}) ## ## Return a k x n matrix of ||x - v||^2 values (the squares of the ## distances between input data points x and cluster centers v), where ## k is the number of cluster centers and n is the number of data points. ## ## The element sqr_dist(i, j) will contain the square of the distance ## between the cluster center V(i, :) and the data point X(j, :). ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy private ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: square_dist_matrix.m ## Last-Modified: 5 Jun 2024 function sqr_dist = square_distance_matrix (X, V) sqr_dist = (sumsq (X, 2) + (sumsq (V, 2))' - 2 * X * V')'; endfunction %!test %! ## Test the faster version of this function (above) by comparing its %! ## output with the output of the previous, nested-for-loop version (below). %! ## %! ## The test is run 100 times (but is reported by the Octave interpreter as %! ## "1 test"). In each of the 100 test runs, the vectorized and loop versions %! ## of the function are called using randomly generated matrices X, V. %! ## %! ## The sizes of X and V, however, aren't random: X has 100 rows, 8 cols, %! ## and V has 5 rows, 8 cols. That is, the entries in X and V are random %! ## values in the range [0, 1], but the sizes of X and V are hard-coded. %! ## %! ## The test is passed if all entries of the two results differ by less than %! ## a tolerance of 10e-9 in all 100 test runs. %! %! function sqr_dist = square_distance_matrix_using_for_loops (X, V) %! k = rows (V); %! n = rows (X); %! sqr_dist = zeros (k, n); %! for i = 1 : k %! Vi = V(i, :); %! for j = 1 : n %! Vi_to_Xj = X(j, :) - Vi; %! sqr_dist(i, j) = sum (Vi_to_Xj .* Vi_to_Xj); %! endfor %! endfor %! endfunction %! %! ## Fixed array sizes and tolerance for the test. %! %! n = 100; %! f = 8; %! k = 5; %! tolerance = 10e-9; %! %! ## Run the test 100 times, in a loop. Each test run is successful if %! ## the vectorized and nested-for-loop version of the function produce %! ## results within the hard-coded tolerance. %! %! for i = 1 : 100 %! X = rand (n, f); %! V = rand (k, f); %! vec_result = square_distance_matrix (X, V); %! loop_result = square_distance_matrix_using_for_loops (X, V); %! assert (abs (vec_result - loop_result) < tolerance) %! endfor fuzzy-logic-toolkit-0.6.1/inst/private/update_cluster_membership.m000066400000000000000000000116211466512601400255340ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{Mu} =} update_cluster_membership (@var{V}, @var{X}, @var{m}, @var{k}, @var{n}, @var{sqr_dist}) ## ## Compute Mu for each (cluster center, input point) pair. ## ## @seealso{fcm, gustafson_kessel, init_cluster_prototypes, update_cluster_prototypes, compute_cluster_obj_fcn, compute_cluster_convergence} ## ## @end deftypefn ## Authors: Tony Trew, L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy partition clustering ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: update_cluster_membership.m ## Last-Modified: 5 Jun 2024 ##---------------------------------------------------------------------- ## Note: This function is an implementation of Equation 13.4 in ## Fuzzy Logic: Intelligence, Control and Information, by ## J. Yen and R. Langari, Prentice Hall, 1999, page 380 ## (International Edition) and Step 3 of Algorithm 4.1 in ## Fuzzy and Neural Control, by Robert Babuska, November 2009, ## p. 63. ##---------------------------------------------------------------------- function Mu = update_cluster_membership (V, X, m, k, n, sqr_dist) sqr_dist_zeros = (sqr_dist == 0); num_zeros = sum (sum (sqr_dist_zeros)); if (num_zeros == 0) exponent = 1.0 / (m - 1); summation = (sqr_dist ./ sum(sqr_dist)).^exponent; if (all (all (summation != 0))) Mu = 1.0 ./ summation; Mu ./= sum (Mu); else error ("division by 0 in update_cluster_membership'\n"); endif else Mu = sqr_dist_zeros / num_zeros; endif endfunction %!test %! ## Test the vectorized version of this function (above) by comparing its %! ## output with the output of the previous, nested-for-loop version (below). %! ## %! ## The test is run 100 times (but is reported by the Octave interpreter as %! ## "1 test"). In each of the 100 test runs, the vectorized and loop versions %! ## of the function are called using randomly generated matrices X, V. %! ## %! ## The sizes of X and V, however, aren't random: X has 100 rows, 8 cols, %! ## and V has 5 rows, 8 cols. That is, the entries in X and V are random %! ## values in the range [0, 1], but the sizes of X and V are hard-coded. %! ## %! ## The test is passed if all entries of the two results differ by less than %! ## a tolerance of 10e-9 in all 100 test runs. %! %! function Mu = update_cluster_membership_using_for_loops (V, X, m, k, n, sqr_dist) %! %! Mu = zeros (k, n); %! %! if (min (min (sqr_dist)) > 0) %! exponent = 1.0 / (m - 1); %! for i = 1 : k %! for j = 1 : n %! summation = 0.0; %! for l = 1 : k %! summation += (sqr_dist(i, j) / sqr_dist(l, j))^exponent; %! endfor %! if (summation != 0) %! Mu(i, j) = 1.0 / summation; %! else %! error ("division by 0 in update_cluster_membership'\n"); %! endif %! endfor %! endfor %! %! else %! num_zeros = 0; %! for i = 1 : k %! for j = 1 : n %! if (sqr_dist(i, j) == 0) %! num_zeros++; %! Mu(i, j) = 1.0; %! endif %! endfor %! endfor %! Mu = Mu / num_zeros; %! endif %! %! endfunction %! %! ## Fixed array sizes, exponent, and tolerance for the test. %! %! n = 100; %! f = 8; %! k = 5; %! m = 2; %! tolerance = 10e-9; %! %! ## Run the test 100 times, in a loop. In the last 5 test runs, make 3 of %! ## the data points in X identical to cluster centers in V in order to test %! ## the else case in the function. %! %! ## Each test run is successful if the vectorized and nested-for-loop %! ## version of the function produce results within the hard-coded tolerance. %! %! for i = 1 : 100 %! X = rand (n, f); %! V = rand (k, f); %! %! if (i > 95) %! X(1:3) = V(1:3); %! endif %! %! sqr_dist = square_distance_matrix (X, V); %! vec_result = update_cluster_membership (V, X, m, k, n, sqr_dist); %! loop_result = update_cluster_membership_using_for_loops (V, X, m, k, n, sqr_dist); %! assert (abs (vec_result - loop_result) < tolerance) %! endfor fuzzy-logic-toolkit-0.6.1/inst/private/update_cluster_prototypes.m000066400000000000000000000040471466512601400256350ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{V} =} update_cluster_prototypes (@var{Mu_m}, @var{X}, @var{k}) ## ## Update the cluster centers to correspond to the given membership ## function values. ## ## @seealso{fcm, gustafson_kessel, init_cluster_prototypes, update_cluster_membership, compute_cluster_obj_fcn, compute_cluster_convergence} ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy partition clustering ## Directory: fuzzy-logic-toolkit/inst/private/ ## Filename: update_cluster_prototypes.m ## Last-Modified: 2 Sep 2012 ##---------------------------------------------------------------------- ## Note: This function is an implementation of Equation 13.5 in ## Fuzzy Logic: Intelligence, Control and Information, by ## J. Yen and R. Langari, Prentice Hall, 1999, page 380 ## (International Edition). ##---------------------------------------------------------------------- function V = update_cluster_prototypes (Mu_m, X, k) V = Mu_m * X; sum_Mu_m = sum (Mu_m'); if (prod (sum_Mu_m) == 0) error ("division by 0 in function update_cluster_prototypes\n"); endif for i = 1 : k V(i, :) /= sum_Mu_m(i); endfor endfunction fuzzy-logic-toolkit-0.6.1/inst/psigmf.m000066400000000000000000000114421466512601400201120ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} psigmf (@var{x}, @var{params}) ## @deftypefnx {Function File} {@var{y} =} psigmf (@var{[x1 x2 ... xn]}, @var{[a1 c1 a2 c2]}) ## ## For a given domain @var{x} and parameters @var{params} (or ## @var{[a1 c1 a2 c2]}), return the corresponding @var{y} values for the product ## of two sigmoidal membership functions. ## ## The argument @var{x} must be a real number or a non-empty vector of strictly ## increasing real numbers, and @var{a1}, @var{c1}, @var{a2}, and @var{c2} must ## be real numbers. This membership function satisfies the equation: ## ## @verbatim ## f(x) = (1/(1 + exp(-a1*(x - c1)))) * (1/(1 + exp(-a2*(x - c2)))) ## @end verbatim ## ## The function is bounded above by 1 and below by 0. ## ## If @var{a1} is positive, @var{a2} is negative, and @var{c1} and @var{c2} are ## far enough apart with @var{c1} < @var{c2}, then: ## ## @verbatim ## (a1)/4 ~ the rising slope at c1 ## c1 ~ the left inflection point ## (a2)/4 ~ the falling slope at c2 ## c2 ~ the right inflection point ## @end verbatim ## ## and at each inflection point, the value of the function is about 0.5: ## ## @verbatim ## f(c1) ~ f(c2) ~ 0.5. ## @end verbatim ## ## (Here, the symbol ~ means "approximately equal".) ## ## To run the demonstration code, type "@t{demo psigmf}" (without the quotation ## marks) at the Octave prompt. ## ## @seealso{dsigmf, gauss2mf, gaussmf, gbellmf, pimf, sigmf, smf, trapmf, trimf, zmf} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy membership sigmoidal ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: psigmf.m ## Last-Modified: 13 Jun 2024 function y = psigmf (x, params) ## If the caller did not supply 2 argument values with the correct ## types, print an error message and halt. if (nargin != 2) error ("psigmf requires 2 arguments\n"); elseif (!is_domain (x)) error ("psigmf's first argument must be a valid domain\n"); elseif (!are_mf_params ('psigmf', params)) error ("psigmf's second argument must be a parameter vector\n"); endif ## Calculate and return the y values of the membership function on ## the domain x. a1 = params(1); c1 = params(2); a2 = params(3); c2 = params(4); y_val = @(x_val) 1 / (1 + exp (-a1 * (x_val - c1))) * ... 1 / (1 + exp (-a2 * (x_val - c2))); y = arrayfun (y_val, x); endfunction %!demo %! x = 0:100; %! params = [0.5 20 -0.3 60]; %! y1 = psigmf(x, params); %! params = [0.3 20 -0.2 60]; %! y2 = psigmf(x, params); %! params = [0.2 20 -0.1 60]; %! y3 = psigmf(x, params); %! figure('NumberTitle', 'off', 'Name', 'psigmf demo'); %! plot(x, y1, 'r;params = [0.5 20 -0.3 60];', 'LineWidth', 2) %! hold on; %! plot(x, y2, 'b;params = [0.3 20 -0.2 60];', 'LineWidth', 2) %! hold on; %! plot(x, y3, 'g;params = [0.2 20 -0.1 60];', 'LineWidth', 2) %! ylim([-0.1 1.1]); %! xlabel('Crisp Input Value', 'FontWeight', 'bold'); %! ylabel('Degree of Membership', 'FontWeight', 'bold'); %! grid; %!test %! x = 0:10:100; %! params = [0.3 20 -0.2 60]; %! y = [2.4726e-03 0.047424 0.4998 0.9502 0.9796 0.8807 ... %! 0.5000 0.1192 0.017986 2.4726e-03 3.3535e-04]; %! z = psigmf(x, params); %! assert(z, y, 1e-4); ## Test input validation %!error %! psigmf() %!error %! psigmf(1) %!error %! psigmf(1, 2, 3) %!error %! psigmf([1 0], 2) %!error %! psigmf(1, 2) %!error %! psigmf(0:100, []) %!error %! psigmf(0:100, [30]) %!error %! psigmf(0:100, [2 3]) %!error %! psigmf(0:100, [90 80 30]) %!error %! psigmf(0:100, 'abc') fuzzy-logic-toolkit-0.6.1/inst/readfis.m000066400000000000000000000533421466512601400202470ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{fis} =} readfis () ## @deftypefnx {Function File} {@var{fis} =} readfis (@var{filename}) ## ## Read the information in an FIS file, and using this information, create and ## return an FIS structure. If called without any arguments or with an empty ## string as an argument, present the user with a file dialog GUI. If called ## with a @var{filename} that does not end with '.fis', append '.fis' to the ## @var{filename}. The @var{filename} is expected to be a string. ## ## Six examples of the input file format and example scripts that use readfis: ## ## @multitable @columnfractions .45 .45 ## @headitem Example FIS File @tab Corresponding Example Script ## @item cubic_approximator.fis ## @tab cubic_approx_demo.m ## @item heart_disease_risk.fis ## @tab heart_disease_demo_2.m ## @item investment_portfolio.fis ## @tab investment_portfolio_demo.m ## @item linear_tip_calculator.fis ## @tab linear_tip_demo.m ## @item mamdani_tip_calculator.fis ## @tab mamdani_tip_demo.m ## @item sugeno_tip_calculator.fis ## @tab sugeno_tip_demo.m ## @end multitable ## @sp 1 ## @seealso{writefis} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: readfis.m ## Last-Modified: 12 Jun 2024 function fis = readfis (filename = '') ## If readfis was not called with 0 or 1 arguments, or if the argument ## is not a string, print an error message and halt. if (nargin > 1) error ("readfis requires 0 or 1 arguments\n"); elseif ((nargin == 1) && !is_string (filename)) error ("readfis's argument must be a string\n"); endif ## Open the input file. fid = open_input_file (filename); ## Read the [System], [Input], [Output], and [Rules] ## sections of the input file. [fis, num_inputs, num_outputs, num_rules, line_num] = ... init_fis_struct (fid); [fis, line_num] = read_fis_inputs (fid, fis, num_inputs, line_num); [fis, line_num] = read_fis_outputs (fid, fis, num_outputs, line_num); fis = read_rules (fid, fis, num_inputs, num_outputs, num_rules, ... line_num); ## Close the input file. fclose (fid); endfunction ##---------------------------------------------------------------------- ## Function: open_input_file ## Purpose: Open the input file specified by the filename. If the ## filename does not end with ".fis", then append ".fis" to ## the filename before opening. Return an fid if successful. ## Otherwise, print an error message and halt. ##---------------------------------------------------------------------- function fid = open_input_file (filename) ##-------------------------------------------------------------------- ## If the filename is not empty, and if the last four characters of ## the filename are not '.fis', append '.fis' to the filename. If the ## filename is empty, use a dialog to select the input file. ##-------------------------------------------------------------------- fn_len = length (filename); if (fn_len == 0) dialog = 1; else dialog = 0; endif if (((fn_len >= 4) && ... !strcmp(".fis",filename(fn_len-3:fn_len))) || ... ((fn_len > 0) && (fn_len < 4))) filename = [filename ".fis"]; elseif (dialog) system_command = sprintf ("zenity --file-selection; echo $file", ... filename); [dialog_error, filename] = system (file = system_command); if (dialog_error) puts ("Type 'help readfis' for more information.\n"); error ("error selecting file using dialog\n"); endif filename = strtrim (filename); endif ##-------------------------------------------------------------------- ## Open input file. ##-------------------------------------------------------------------- [fid, msg] = fopen (filename, "r"); if (fid == -1) if (dialog) system ('zenity --error --text "Error opening input file."'); endif puts ("Type 'help readfis' for more information.\n"); printf ("Error opening input file: %s\n", msg); error ("error opening input file\n"); endif endfunction ##---------------------------------------------------------------------- ## Function: init_fis_struct ## Purpose: Read the [System] section of the input file. Using the ## strings read from the input file, create a new FIS. If an ## error in the format of the input file is found, print an ## error message and halt. ##---------------------------------------------------------------------- function [fis, num_inputs, num_outputs, num_rules, line_num] = ... init_fis_struct (fid) ##-------------------------------------------------------------------- ## Read the [System] section. ##-------------------------------------------------------------------- line_num = 1; [line, line_num] = get_line (fid, line_num); [line, line_num] = get_line (fid, line_num); [fis_name, count] = sscanf (line, "Name = '%s", "C"); if (count != 1) error ("line %d: name of FIS expected\n", --line_num); endif fis_name = trim_last_char (fis_name); [line, line_num] = get_line (fid, line_num); [fis_type, count] = sscanf (line, "Type = '%s", "C"); if (count != 1) error ("line %d: type of FIS expected\n", --line_num); endif fis_type = trim_last_char (fis_type); [line, line_num] = get_line (fid, line_num); [fis_version, count] = sscanf (line, "Version = %f", "C"); if (count != 1) error ("line %d: version of FIS expected\n", --line_num); endif [line, line_num] = get_line (fid, line_num); [num_inputs, count] = sscanf (line, "NumInputs = %d", "C"); if (count != 1) error ("line %d: number of inputs expected\n", --line_num); endif [line, line_num] = get_line (fid, line_num); [num_outputs, count] = sscanf (line, "NumOutputs = %d", "C"); if (count != 1) error ("line %d: number of oututs expected\n", --line_num); endif [line, line_num] = get_line (fid, line_num); [num_rules, count] = sscanf (line, "NumRules = %d", "C"); if (count != 1) error ("line %d: number of rules expected\n", --line_num); endif [line, line_num] = get_line (fid, line_num); [and_method, count] = sscanf (line, "AndMethod = '%s", "C"); if (count != 1) error ("line %d: and method expected\n", --line_num); endif and_method = trim_last_char (and_method); [line, line_num] = get_line (fid, line_num); [or_method, count] = sscanf (line, "OrMethod = '%s", "C"); if (count != 1) error ("line %d: or method expected\n", --line_num); endif or_method = trim_last_char (or_method); [line, line_num] = get_line (fid, line_num); [imp_method, count] = sscanf (line, "ImpMethod = '%s", "C"); if (count != 1) error ("line %d: implication method expected\n", --line_num); endif imp_method = trim_last_char (imp_method); [line, line_num] = get_line (fid, line_num); [agg_method, count] = sscanf (line, "AggMethod = '%s", "C"); if (count != 1) error ("line %d: aggregation method expected\n", --line_num); endif agg_method = trim_last_char (agg_method); [line, line_num] = get_line (fid, line_num); [defuzz_method, count] = sscanf (line, "DefuzzMethod = '%s", "C"); if (count != 1) error ("line %d: defuzzification method expected\n", --line_num); endif defuzz_method = trim_last_char (defuzz_method); ##-------------------------------------------------------------------- ## Create a new FIS structure using the strings read from the ## input file. ##-------------------------------------------------------------------- fis = struct ('name', fis_name, ... 'type', fis_type, ... 'version', fis_version, ... 'andMethod', and_method, ... 'orMethod', or_method, ... 'impMethod', imp_method, ... 'aggMethod', agg_method, ... 'defuzzMethod', defuzz_method, ... 'input', [], ... 'output', [], ... 'rule', []); endfunction ##---------------------------------------------------------------------- ## Function: read_fis_inputs ## Purpose: For each FIS input, read the [Input] section from ## file. Add each new input and its membership functions to ## the FIS structure. ##---------------------------------------------------------------------- function [fis, line_num] = read_fis_inputs (fid, fis, num_inputs, ... line_num) for i = 1 : num_inputs [next_fis_input, num_mfs, line_num] = ... get_next_fis_io (fid, line_num, i, 'input'); if (i == 1) fis.input = next_fis_input; else fis.input = [fis.input, next_fis_input]; endif ##------------------------------------------------------------------ ## Read membership function info for the current FIS input from ## file. Add each new membership function to the FIS struct. ##------------------------------------------------------------------ for j = 1 : num_mfs [next_mf, line_num] = get_next_mf (fid, line_num, i, j, 'input'); if (j == 1) fis.input(i).mf = next_mf; else fis.input(i).mf = [fis.input(i).mf, next_mf]; endif endfor endfor endfunction ##---------------------------------------------------------------------- ## Function: read_fis_outputs ## Purpose: For each FIS output, read the [Output] section from ## file. Add each new output and its membership functions to ## the FIS structure. ##---------------------------------------------------------------------- function [fis, line_num] = read_fis_outputs (fid, fis, num_outputs, ... line_num) for i = 1 : num_outputs [next_fis_output, num_mfs, line_num] = ... get_next_fis_io (fid, line_num, i, 'output'); if (i == 1) fis.output = next_fis_output; else fis.output = [fis.output, next_fis_output]; endif ##------------------------------------------------------------------ ## Read membership function info for the current FIS output from ## file. Add each new membership function to the FIS struct. ##------------------------------------------------------------------ for j = 1 : num_mfs [next_mf, line_num] = get_next_mf (fid, line_num, i, j, 'output'); if (j == 1) fis.output(i).mf = next_mf; else fis.output(i).mf = [fis.output(i).mf, next_mf]; endif endfor endfor endfunction ##---------------------------------------------------------------------- ## Function: read_rules ## Purpose: Read the [Rules] section from file, and add the rules to ## the FIS. ##---------------------------------------------------------------------- function fis = read_rules (fid, fis, num_inputs, num_outputs, ... num_rules, line_num) [line, line_num] = get_line (fid, line_num); for i = 1 : num_rules [next_rule, line_num] = ... get_next_rule (fid, line_num, num_inputs, num_outputs); if (i == 1) fis.rule = next_rule; else fis.rule = [fis.rule, next_rule]; endif endfor endfunction ##---------------------------------------------------------------------- ## Function: get_next_fis_io ## Purpose: Read the next [Input] or [Output] section of the ## input file. Using the info read from the input file, create ## a new FIS input or output structure. If an error in the ## format of the input file is found, print an error message ## and halt. ##---------------------------------------------------------------------- function [next_fis_io, num_mfs, line_num] = ... get_next_fis_io (fid, line_num, i, in_or_out) ##-------------------------------------------------------------------- ## Read [Input] or [Output] section from file. ##-------------------------------------------------------------------- [line, line_num] = get_line (fid, line_num); if (strcmp ('input', in_or_out)) [io_index, count] = sscanf (line, "[Input %d", "C"); else [io_index, count] = sscanf (line, "[Output %d", "C"); endif if ((count != 1) || (io_index != i)) error ("line %d: next input or output expected\n", --line_num); endif [line, line_num] = get_line (fid, line_num); [var_name, count] = sscanf (line, "Name = '%s", "C"); if (count != 1) error ("line %d: name of %s %d expected\n", --line_num, ... in_or_out, i); endif var_name = trim_last_char (var_name); [line, line_num] = get_line (fid, line_num); [range_low, range_high, count] = sscanf (line, ... "Range = [ %f %f ]", "C"); if ((count != 2) || (range_low > range_high)) error ("line %d: range for %s %d expected\n", --line_num, ... in_or_out, i); endif [line, line_num] = get_line (fid, line_num); [num_mfs, count] = sscanf (line, "NumMFs = %d", "C"); if (count != 1) error ("line %d: number of MFs for %s %d expected\n", ... --line_num, in_or_out, i); endif ##-------------------------------------------------------------------- ## Create a new FIS input or output structure. ##-------------------------------------------------------------------- next_fis_io = struct ('name', var_name, 'range', ... [range_low, range_high], 'mf', []); endfunction ##---------------------------------------------------------------------- ## Function: get_next_mf ## Purpose: Read information specifying the jth membership function for ## Input or Output (if in_or_out is 'input' or 'output', ## respectively) from the input file. Create a new membership ## function structure using the info read. If an error in the ## format of the input file is found, print an error message ## and halt. ##---------------------------------------------------------------------- function [next_mf, line_num] = get_next_mf (fid, line_num, i, j, ... in_or_out) ##-------------------------------------------------------------------- ## Read membership function info for the new FIS input or output ## from file. ##-------------------------------------------------------------------- [line, line_num] = get_line (fid, line_num); if (compare_versions (OCTAVE_VERSION(), "3.8.0", ">=")) line_vec = discard_empty_strings (ostrsplit (line, "=':,[] \t", true)); else line_vec = discard_empty_strings (strsplit (line, "=':,[] \t", true)); endif mf_index = sscanf (line_vec{1}, "MF %d", "C"); mf_name = line_vec{2}; mf_type = line_vec{3}; if (mf_index != j) error ("line %d: next MF for %s %d expected\n", --line_num, in_or_out, i); endif j = 1; for i = 4 : length (line_vec) [mf_params(j++), count] = sscanf (line_vec{i}, "%f", "C"); if (count != 1) error ("line %d: %s %d MF%d params expected\n", --line_num, in_or_out, i, j); endif endfor ##-------------------------------------------------------------------- ## Create a new membership function structure. ##-------------------------------------------------------------------- next_mf = struct ('name', mf_name, 'type', mf_type, 'params', ... mf_params); endfunction ##---------------------------------------------------------------------- ## Function: get_next_rule ## Purpose: Read the next rule from the input file. Create a struct for ## the new rule. If an error in the format of the input file ## is found, print an error message and halt. ##---------------------------------------------------------------------- function [next_rule, line_num] = get_next_rule (fid, line_num, ... num_inputs, num_outputs) [line, line_num] = get_line (fid, line_num); if (compare_versions (OCTAVE_VERSION(), "3.8.0", ">=")) line_vec = ostrsplit (line, ",():", true); else line_vec = strsplit (line, ",():", true); endif ##-------------------------------------------------------------------- ## Read antecedent. ##-------------------------------------------------------------------- format_str = ""; for j = 1 : num_inputs format_str = [format_str " %f"]; endfor [antecedent, count] = sscanf (line_vec{1}, format_str, ... [1, num_inputs]); if (length (antecedent) != num_inputs) error ("Line %d: Rule antecedent expected.\n", line_num); endif ##-------------------------------------------------------------------- ## Read consequent. ##-------------------------------------------------------------------- format_str = ""; for j = 1 : num_outputs format_str = [format_str " %f"]; endfor [consequent, count] = sscanf (line_vec{2}, format_str, ... [1, num_outputs]); if (length (consequent) != num_outputs) error ("Line %d: Rule consequent expected.\n", line_num); endif ##-------------------------------------------------------------------- ## Read weight. ##-------------------------------------------------------------------- [weight, count] = sscanf (line_vec{3}, "%f", "C"); if (count != 1) error ("Line %d: Rule weight expected.\n", line_num); endif ##-------------------------------------------------------------------- ## Read connection. ##-------------------------------------------------------------------- [connection, count] = sscanf (line_vec{5}, "%d", "C"); if ((count != 1) || (connection < 1) || (connection > 2)) error ("Line %d: Antecedent connection expected.\n", line_num); endif ##-------------------------------------------------------------------- ## Create a new rule struct. ##-------------------------------------------------------------------- next_rule = struct ('antecedent', antecedent, ... 'consequent', consequent, ... 'weight', weight, ... 'connection', connection); endfunction ##---------------------------------------------------------------------- ## Function: get_line ## Purpose: Read the next line of the input file (without the newline) ## into line. Print an error message and halt on eof. ##---------------------------------------------------------------------- function [line, line_num] = get_line (fid, line_num) do line = fgetl (fid); if (isequal (line, -1)) error ("unexpected end of file at line %d", line_num); endif line = trim_leading_whitespace (line); line_num++; until (!comment_or_empty (line)) endfunction ##---------------------------------------------------------------------- ## Function: discard_empty_strings ## Purpose: Return a copy of the input cell array without any ## empty string elements. ##---------------------------------------------------------------------- function ret_val = discard_empty_strings (cell_array) ret_val = {}; j = 1; for i = 1 : length (cell_array) if (!strcmp (cell_array{i}, "")) ret_val{j++} = cell_array{i}; endif endfor endfunction ##---------------------------------------------------------------------- ## Function: trim_last_char ## Purpose: Return a copy of the input string without its final ## character. ##---------------------------------------------------------------------- function str = trim_last_char (str) str = str(1 : length (str) - 1); endfunction ##---------------------------------------------------------------------- ## Function: trim_leading_whitespace ## Purpose: Return a copy of the input string without leading ## whitespace. ##---------------------------------------------------------------------- function str = trim_leading_whitespace (str) str_length = length (str); i = 1; while (i <= str_length && ... (str (i) == ' ' || str (i) == '\t' || str (i) == '\n' || ... str (i) == '\f' || str (i) == '\r' || str (i) == '\v')) i++; endwhile if (i > str_length) str = ""; else str = str (i : str_length); endif endfunction ##---------------------------------------------------------------------- ## Function: comment_or_empty ## Purpose: Return true if the line is a comment (that is, it begins ## with '#' or '%') or an empty line, and return false ## otherwise. It is assumed that leading whitespace has been ## removed from the input line. ##---------------------------------------------------------------------- function ret_val = comment_or_empty (line) ret_val = (length (line) == 0) || (line (1) == '#') || ... (line (1) == '%'); endfunction %!shared fis %! fis = readfis ('sugeno_tip_calculator.fis'); %!assert(fis.andMethod == 'einstein_product'); %!assert(fis.orMethod == 'einstein_sum'); %!assert(fis.impMethod == 'prod'); %!assert(fis.aggMethod == 'sum'); %!assert(fis.defuzzMethod == 'wtaver'); ## Test input validation %!error %! readfis(1, 2) %!error %! readfis(1) fuzzy-logic-toolkit-0.6.1/inst/rmmf.m000066400000000000000000000100441466512601400175630ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{fis} =} rmmf (@var{fis}, @var{in_or_out}, @var{var_index}, @var{mf}, @var{mf_index}) ## ## Remove a membership function from an existing FIS ## structure and return the updated FIS. ## ## The types/values of the arguments are expected to be: ## ## @multitable @columnfractions .35 .40 ## @headitem Argument @tab Expected Type or Value ## @item @var{fis} ## @tab an FIS structure ## @item @var{in_or_out} ## @tab 'input' or 'output' (case-insensitive) ## @item @var{var_index} ## @tab valid index of an FIS input/output variable ## @item @var{mf} ## @tab the string 'mf' ## @item @var{mf_index} ## @tab an integer ## @end multitable ## @sp 1 ## Note that rmmf will allow the user to delete membership functions that are ## currently in use by rules in the FIS. ## ## @seealso{addmf, rmvar} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy membership ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: rmmf.m ## Last-Modified: 13 Jun 2024 function fis = rmmf (fis, in_or_out, var_index, mf, mf_index) ## If the caller did not supply 5 argument values with the correct ## types, print an error message and halt. if (nargin != 5) error ("rmmf requires 5 arguments\n"); elseif (!is_fis (fis)) error ("rmmf's first argument must be an FIS structure\n"); elseif (!(is_string(in_or_out) && ... ismember (tolower (in_or_out), {'input', 'output'}))) error ("rmmf's second argument must be 'input' or 'output'\n"); elseif (!is_var_index (fis, in_or_out, var_index)) error ("rmmf's third argument must be a variable index\n"); elseif (!isequal (mf, 'mf')) error ("rmmf's fourth argument must be the string 'mf'\n"); elseif (!is_int (mf_index)) error ("rmmf's fifth argument must be an integer\n"); endif ## Delete the membership function struct and update the FIS structure. if (strcmp (tolower (in_or_out), 'input')) all_mfs = fis.input(var_index).mf; fis.input(var_index).mf = [all_mfs(1 : mf_index - 1), ... all_mfs(mf_index + 1 : numel(all_mfs))]; else all_mfs = fis.output(var_index).mf; fis.output(var_index).mf = [all_mfs(1 : mf_index - 1), ... all_mfs(mf_index + 1 : numel(all_mfs))]; endif endfunction %!shared fis %! fis = readfis ('mamdani_tip_calculator.fis'); %!test %! fis = rmmf(fis, 'input', 1, 'mf', 1); %! assert(fis.input(1).mf.name, 'Good'); ## Test input validation %!error %! rmmf() %!error %! rmmf(1) %!error %! rmmf(1, 2) %!error %! rmmf(1, 2, 3) %!error %! rmmf(1, 2, 3, 4) %!error %! rmmf(1, 2, 3, 4, 5, 6) %!error %! rmmf(1, 2, 3, 4, 5) %!error %! rmmf(fis, 2, 3, 4, 5) %!error %! rmmf(fis, 'input', 3, 4, 5) %!error %! rmmf(fis, 'input', 1, 4, 5) %!error %! rmmf(fis, 'input', 1, 'mf', 5.5) fuzzy-logic-toolkit-0.6.1/inst/rmvar.m000066400000000000000000000066001466512601400177540ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{fis} =} rmvar (@var{fis}, @var{in_or_out}, @var{var_index}) ## ## Remove an input or output variable from an existing FIS ## structure and return the updated FIS. ## ## The types/values of the arguments are expected to be: ## ## @multitable @columnfractions .35 .40 ## @headitem Argument @tab Expected Type or Value ## @item @var{fis} ## @tab an FIS structure ## @item @var{in_or_out} ## @tab either 'input' or 'output' (case-insensitive) ## @item @var{var_index} ## @tab an FIS input or output variable index ## @end multitable ## @sp 1 ## Note that rmvar will allow the user to delete an input or output variable ## that is currently in use by rules in the FIS. ## ## @seealso{addvar, rmmf} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy variable ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: rmvar.m ## Last-Modified: 13 Jun 2024 function fis = rmvar (fis, in_or_out, var_index) ## If the caller did not supply 3 argument values with the correct ## types, print an error message and halt. if (nargin != 3) error ("rmvar requires 3 arguments\n"); elseif (!is_fis (fis)) error ("rmvar's first argument must be an FIS structure\n"); elseif (!(is_string (in_or_out) && ... ismember (tolower (in_or_out), {'input', 'output'}))) error ("rmvar's second argument must be 'input' or 'output'\n"); elseif (!is_var_index (fis, in_or_out, var_index)) error ("rmvar's third argument must be a variable index\n"); endif ## Delete the variable struct and update the FIS structure. if (strcmp (tolower (in_or_out), 'input')) all_vars = fis.input; fis.input = [all_vars(1 : var_index - 1), ... all_vars(var_index + 1 : numel (all_vars))]; else all_vars = fis.output; fis.output = [all_vars(1 : var_index - 1), ... all_vars(var_index + 1 : numel (all_vars))]; endif endfunction %!shared fis %! fis = readfis ('mamdani_tip_calculator.fis'); %!test %! fis = rmvar(fis, 'input', 1); %! assert(fis.input.name, 'Service'); ## Test input validation %!error %! rmvar() %!error %! rmvar(1) %!error %! rmvar(1, 2) %!error %! rmvar(1, 2, 3, 4) %!error %! rmvar(1, 2, 3) %!error %! rmvar(fis, 2, 3) %!error %! rmvar(fis, 'input', 3) fuzzy-logic-toolkit-0.6.1/inst/setfis.m000066400000000000000000000250161466512601400201240ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{fis} =} setfis (@var{fis}, @var{property}, @var{property_value}) ## @deftypefnx {Function File} {@var{fis} =} setfis (@var{fis}, @var{in_or_out}, @var{var_index}, @var{var_property}, @var{var_property_value}) ## @deftypefnx {Function File} {@var{fis} =} setfis (@var{fis}, @var{in_or_out}, @var{var_index}, @var{mf}, @var{mf_index}, @var{mf_property}, @var{mf_property_value}) ## ## Set a property (field) value of an FIS structure and return the ## updated FIS. ## ## There are three forms of setfis: ## ## @multitable @columnfractions .20 .70 ## @headitem Number of Arguments @tab Action Taken ## @item 3 ## @tab Set a property of the FIS structure. The properties that may ## be set are: name, type, andmethod, ormethod, impmethod, ## addmethod, defuzzmethod, and version. ## @item 5 ## @tab Set a property of an input or output variable of the FIS ## structure. The properties that may be set are: name and range. ## @item 7 ## @tab Set a property of a membership function. The properties that ## may be set are: name, type, and params. ## @end multitable ## @sp 1 ## The types/values of the arguments are expected to be: ## ## @multitable @columnfractions .20 .70 ## @headitem Argument @tab Expected Type or Value ## @item @var{fis} ## @tab an FIS structure ## @item @var{property} ## @tab a string; one of 'name', 'type', 'andmethod', ## 'ormethod', 'impmethod', 'addmethod', ## 'defuzzmethod', and 'version' (case-insensitive) ## @item @var{property_value} ## @tab a number (if property is 'version'); a string (otherwise) ## @item @var{in_or_out} ## @tab either 'input' or 'output' (case-insensitive) ## @item @var{var_index} ## @tab a valid integer index of an input or output FIS variable ## @item @var{var_property} ## @tab a string; either 'name' or 'range' ## @item @var{var_property_value} ## @tab a string (if var_property is 'name') or ## a vector range (if var_property is 'range') ## @item @var{mf} ## @tab the string 'mf' ## @item @var{mf_index} ## @tab a valid integer index of a membership function ## @item @var{mf_property} ## @tab a string; one of 'name', 'type', or 'params' ## @item @var{mf_property_value} ## @tab a string (if mf_property is 'name' or 'type'); ## an array (if mf_property is 'params') ## @end multitable ## @sp 1 ## Note that all of the strings representing properties above are case ## insensitive. ## ## @seealso{newfis, getfis, showfis} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: setfis.m ## Last-Modified: 13 Jun 2024 ##---------------------------------------------------------------------- function fis = setfis (fis, arg2, arg3, arg4 = 'dummy', ... arg5 = 'dummy', arg6 = 'dummy', arg7 = 'dummy') switch (nargin) case 3 fis = setfis_three_args (fis, arg2, arg3); case 5 fis = setfis_five_args (fis, arg2, arg3, arg4, arg5); case 7 fis = setfis_seven_args (fis, arg2, arg3, arg4, arg5, ... arg6, arg7); otherwise error ("setfis requires 3, 5, or 7 arguments\n"); endswitch endfunction ##---------------------------------------------------------------------- ## Function: setfis_three_args ## Purpose: Handle calls to setfis that have 3 arguments. See the ## comment at the top of this file for more complete info. ##---------------------------------------------------------------------- function fis = setfis_three_args (fis, arg2, arg3) ## If not all of the arguments have the correct types, print an error ## message and halt. if (!is_fis (fis)) error ("setfis's first argument must be an FIS structure\n"); elseif (!(is_string (arg2) && ismember (tolower (arg2), ... {'name', 'type', 'andmethod', 'ormethod', 'impmethod', ... 'aggmethod', 'defuzzmethod', 'version'}))) error ("incorrect second argument to setfis\n"); elseif (strcmp(tolower (arg2), 'version') && !is_real (arg3)) error ("the third argument to setfis must be a number\n"); elseif (!strcmp(tolower (arg2), 'version') && !is_string (arg3)) error ("the third argument to setfis must be a string\n"); endif ## Set the property (arg2) of the FIS to the property value (arg3). switch (tolower(arg2)) case 'name' fis.name = arg3; case 'version' fis.version = arg3; case 'type' fis.type = arg3; case 'andmethod' fis.andMethod = arg3; case 'ormethod' fis.orMethod = arg3; case 'impmethod' fis.impMethod = arg3; case 'aggmethod' fis.aggMethod = arg3; case 'defuzzmethod' fis.defuzzMethod = arg3; endswitch endfunction ##---------------------------------------------------------------------- ## Function: setfis_five_args ## Purpose: Handle calls to setfis that have 5 arguments. See the ## comment at the top of this file for more complete info. ##---------------------------------------------------------------------- function fis = setfis_five_args (fis, arg2, arg3, arg4, arg5) ## If not all of the arguments have the correct types, print an error ## message and halt. if (!is_fis (fis)) error ("setfis's first argument must be an FIS structure\n"); elseif (!(is_string (arg2) && ... ismember (tolower (arg2), {'input','output'}))) error ("setfis's second argument must be 'input' or 'output'\n"); elseif (!is_var_index (fis, arg2, arg3)) error ("setfis's third argument must be a variable index\n"); elseif (!(is_string (arg4) && ... ismember (tolower (arg4), {'name', 'range'}))) error ("setfis's fourth argument must be 'name' or 'range'\n"); elseif (strcmp (arg4, 'name') && !is_string (arg5)) error ("incorrect fifth argument to setfis\n"); elseif (strcmp (arg4, 'range') && !is_real_matrix (arg5)) error ("incorrect fifth argument to setfis\n"); endif ## Set the input or output variable property (arg4) to the ## value (arg5). switch (tolower (arg2)) case 'input' switch (tolower (arg4)) case 'name' fis.input(arg3).name = arg5; case 'range' fis.input(arg3).range = arg5; endswitch case 'output' switch (tolower (arg4)) case 'name' fis.output(arg3).name = arg5; case 'range' fis.output(arg3).range = arg5; endswitch endswitch endfunction ##---------------------------------------------------------------------- ## Function: setfis_seven_args ## Purpose: Handle calls to setfis that have 7 arguments. See the ## comment at the top of this file for more complete info. ##---------------------------------------------------------------------- function fis = setfis_seven_args (fis, arg2, arg3, arg4, arg5, ... arg6, arg7) ## If not all of the arguments have the correct types, print an error ## message and halt. if (!is_fis (fis)) error ("setfis's first argument must be an FIS structure\n"); elseif (!(is_string (arg2) && ... ismember (tolower (arg2), {'input','output'}))) error ("setfis's second argument must be 'input' or 'output'\n"); elseif (!is_var_index (fis, arg2, arg3)) error ("setfis's third argument must be a variable index\n"); elseif (!(is_string (arg4) && strcmp (tolower (arg4), 'mf'))) error ("setfis's fourth argument must be 'mf'\n"); elseif (!is_mf_index (fis, arg2, arg3, arg5)) error ("setfis's fifth arg must be a membership function index\n"); elseif (!(is_string (arg6) && ismember (tolower(arg6), ... {'name', 'type', 'params'}))) error ("incorrect sixth argument to setfis\n"); elseif (ismember (tolower (arg6), {'name', 'type'}) && ... !is_string (arg7)) error ("incorrect seventh argument to setfis\n"); elseif (strcmp (tolower (arg6), 'params') && !is_real_matrix (arg7)) error ("incorrect seventh argument to setfis\n"); endif ## Set the membership function property (arg6) to the value (arg7). switch (tolower (arg2)) case 'input' switch (tolower (arg6)) case 'name' fis.input(arg3).mf(arg5).name = arg7; case 'type' fis.input(arg3).mf(arg5).type = arg7; case 'params' fis.input(arg3).mf(arg5).params = arg7; endswitch case 'output' switch (tolower (arg6)) case 'name' fis.output(arg3).mf(arg5).name = arg7; case 'type' fis.output(arg3).mf(arg5).type = arg7; case 'params' fis.output(arg3).mf(arg5).params = arg7; endswitch endswitch endfunction %!shared fis %! fis = readfis ('mamdani_tip_calculator.fis'); %!test %! fis = setfis(fis, 'defuzzMethod', 'mom'); %! assert(fis.defuzzMethod, 'mom'); ## Test input validation %!error %! setfis() %!error %! setfis(1) %!error %! setfis(1, 2) %!error %! setfis(1, 2, 3, 4) %!error %! setfis(1, 2, 3, 4, 5, 6) %!error %! setfis(1, 2, 3, 4, 5, 6, 7, 8) %!error %! setfis(1, 2, 3, 4, 5, 6, 7) %!error %! setfis(fis, 2, 3, 4, 5, 6, 7) %!error %! setfis(fis, 'input', 3, 4, 5, 6, 7) %!error %! setfis(fis, 'input', 1, 4, 5, 6, 7) %!error %! setfis(fis, 'input', 1, 'mf', 5, 6, 7) %!error %! setfis(fis, 'input', 1, 'mf', 1, 6, 7) %!error %! setfis(fis, 'input', 1, 'mf', 1, 'name', 7) fuzzy-logic-toolkit-0.6.1/inst/showfis.m000066400000000000000000000220151466512601400203050ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {} showfis (@var{fis}) ## ## Print all of the property (field) values of the FIS structure and its ## substructures. ## ## @seealso{getfis, showrule} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: showfis.m ## Last-Modified: 29 May 2024 function showfis (fis) ## If getfis was called with an incorrect number of arguments, ## or the argument does not have the correct type, print an error ## message and halt. if (nargin != 1) error ("showfis requires 1 argument\n"); elseif (!is_fis (fis)) error ("showfis's argument must be an FIS structure\n"); endif ## Print properties of the FIS structure. ## Determine: ## the number of input variables ## number of output variables ## number of rules ## input membership function names ## input membership function types ## input membership functions parameters ## number of input membership functions ## output membership function names ## output membership function types ## output membership function parameters ## number of output membership functions num_inputs = columns(fis.input); num_outputs = columns(fis.output); num_rules = columns(fis.rule); k = 1; in_mf_labels = {}; in_mf_types = {}; in_mf_params{k} = []; for i = 1 : num_inputs for j = 1 : columns (fis.input(i).mf) in_mf_labels{k} = fis.input(i).mf(j).name; in_mf_types{k} = fis.input(i).mf(j).type; in_mf_params{k++} = fis.input(i).mf(j).params; endfor endfor num_input_mf = k - 1; k = 1; out_mf_labels = {}; out_mf_types = {}; out_mf_params{k} = []; for i = 1 : num_outputs for j = 1 : columns (fis.output(i).mf) out_mf_labels{k} = fis.output(i).mf(j).name; out_mf_types{k} = fis.output(i).mf(j).type; out_mf_params{k++} = fis.output(i).mf(j).params; endfor endfor num_output_mf = k - 1; ## Print the name, type, and number of inputs/outputs. line = 1; printf ("%d. Name %s\n", line++, fis.name); printf ("%d. Type %s\n", line++, fis.type); printf ("%d. Inputs/Outputs [%d %d]\n", line++, num_inputs, ... num_outputs); ## Print the number of input membership functions. printf ("%d. NumInputMFs ", line++); if (num_inputs == 0) printf ("0\n"); elseif (num_inputs == 1) printf ("%d\n", columns(fis.input(1).mf)); else printf("["); for i = 1 : num_inputs-1 printf ("%d ", columns(fis.input(i).mf)); endfor printf ("%d]\n", columns(fis.input(num_inputs).mf)); endif ## Print the number of output membership functions. printf ("%d. NumOutputMFs ", line++); if (num_outputs == 0) printf("0\n"); elseif (num_outputs == 1) printf ("%d\n", columns(fis.output(1).mf)); else printf ("["); for i = 1 : num_outputs - 1 printf ("%d ", columns (fis.output(i).mf)); endfor printf ("%d]\n", columns (fis.output(num_outputs).mf)); endif ## Print the number of rules, 'And' method, 'Or' method, 'Implication' ## method, 'Aggregation' method, and 'Defuzzification' method. printf ("%d. NumRules %d\n", line++, num_rules); printf ("%d. AndMethod %s\n", line++, fis.andMethod); printf ("%d. OrMethod %s\n", line++, fis.orMethod); printf ("%d. ImpMethod %s\n", line++, fis.impMethod); printf ("%d. AggMethod %s\n", line++, fis.aggMethod); printf ("%d. DefuzzMethod %s\n", line++, fis.defuzzMethod); ## Print the input variable names (labels). printf ("%d. InLabels ", line++); if (num_inputs == 0) printf ("\n"); else printf ("%s\n", fis.input(1).name); for i = 2 : num_inputs printf ("%d. %s\n", line++, fis.input(i).name); endfor endif ## Print the output variable names (labels). printf ("%d. OutLabels ", line++); if (num_outputs == 0) printf ("\n"); else printf ("%s\n", fis.output(1).name); for i = 2 : num_outputs printf ("%d. %s\n", line++, fis.output(i).name); endfor endif ## Print the ranges of the input variables. printf ("%d. InRange ", line++); if (num_inputs == 0) printf ("\n"); else printf ("%s\n", mat2str(fis.input(1).range)); for i = 2 : num_inputs printf ("%d. ", line++); printf ("%s\n", mat2str(fis.input(i).range)); endfor endif ## Print the ranges of the output variables. printf ("%d. OutRange ", line++); if (num_outputs == 0) printf ("\n"); else printf ("%s\n", mat2str(fis.output(1).range)); for i = 2 : num_outputs printf ("%d. ", line++); printf ("%s\n", mat2str (fis.output(i).range)); endfor endif ## Print the input variables' membership function labels. printf ("%d. InMFLabels ", line++); if (num_input_mf == 0) printf ("\n"); else printf ("%s\n", in_mf_labels{1}); for i = 2 : num_input_mf printf ("%d. %s\n", line++, in_mf_labels{i}); endfor endif ## Print the output variables' membership function labels. printf ("%d. OutMFLabels ", line++); if (num_output_mf == 0) printf ("\n"); else printf ("%s\n", out_mf_labels{1}); for i = 2 : num_output_mf printf ("%d. %s\n", line++, out_mf_labels{i}); endfor endif ## Print the input variables' membership function types. printf ("%d. InMFTypes ", line++); if (num_input_mf == 0) printf ("\n"); else printf ("%s\n", in_mf_types{1}); for i = 2 : num_input_mf printf ("%d. %s\n", line++, in_mf_types{i}); endfor endif ## Print the output variables' membership function types. printf ("%d. OutMFTypes ", line++); if (num_output_mf == 0) printf ("\n"); else printf ("%s\n", out_mf_types{1}); for i = 2 : num_output_mf printf ("%d. %s\n", line++, out_mf_types{i}); endfor endif ## Print the input variables' membership function parameters. printf ("%d. InMFParams ", line++); if (num_input_mf == 0) printf ("\n"); else printf ("%s\n", mat2str(in_mf_params{1})); for i = 2 : num_input_mf printf ("%d. ", line++); printf ("%s\n", mat2str (in_mf_params{i})); endfor endif ## Print the output variables' membership function parameters. printf ("%d. OutMFParams ", line++); if (num_output_mf == 0) printf ("\n"); else printf ("%s\n", mat2str (out_mf_params{1})); for i = 2 : num_output_mf printf ("%d. ", line++); printf ("%s\n", mat2str (out_mf_params{i})); endfor endif ## Print the rule antecedents. printf("%d. Rule Antecedent ", line++); if (num_rules == 0) printf ("\n"); else printf ("%s\n", mat2str (fis.rule(1).antecedent)); for i = 2 : num_rules printf ("%d. ", line++); printf ("%s\n", mat2str (fis.rule(i).antecedent)); endfor endif ## Print the rule consequents. printf ("%d. Rule Consequent ", line++); if (num_rules == 0) printf ("\n"); else printf ("%s\n", mat2str (fis.rule(1).consequent)); for i = 2 : num_rules printf ("%d. ", line++); printf ("%s\n", mat2str (fis.rule(i).consequent)); endfor endif ## Print the rule weights. printf("%d. Rule Weight ", line++); if (num_rules == 0) printf ("\n"); else printf ("%d\n", fis.rule(1).weight); for i = 2 : num_rules printf ("%d. %d\n", line++, fis.rule(i).weight); endfor endif ## Print the rule connections. printf ("%d. Rule Connection ", line++); if (num_rules == 0) printf ("\n"); else printf ("%d\n", fis.rule(1).connection); for i = 2 : num_rules printf ("%d. %d\n", line++, ... fis.rule(i).connection); endfor endif endfunction ## Test input validation %!error %! showfis() %!error %! showfis(1, 2) %!error %! showfis(1) fuzzy-logic-toolkit-0.6.1/inst/showrule.m000066400000000000000000000440571466512601400205050ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {} showrule (@var{fis}) ## @deftypefnx {Function File} {} showrule (@var{fis}, @var{index_list}) ## @deftypefnx {Function File} {} showrule (@var{fis}, @var{index_list}, @var{format}) ## @deftypefnx {Function File} {} showrule (@var{fis}, @var{index_list}, @var{'verbose'}, @var{language}) ## @deftypefnx {Function File} {} showrule (@var{fis}, @var{index_list}, @var{'verbose'}, @var{'custom'}, @var{@{"and" "or" "If" "then" "is" "isn't" "somewhat" "very" "extremely" "very very"@}}) ## ## ## Show the rules for an FIS structure in verbose, symbolic, or indexed format. ## Built in languages for the 'verbose' format are: English, ## Chinese (or Mandarin, Pinyin), Russian (or Pycckii, Russkij), French (or Francais), ## Spanish (or Espanol), and German (or Deutsch). The names of the languages are ## case-insensitive, Chinese is written in Pinyin, and Russian is transliterated. ## ## To use a custom language, enter 'verbose' and 'custom' for the third and ## fourth parameters, respectively, and a cell array of ten strings (to specify ## the custom language) corresponding to the English @{"and" "or" "If" "then" ## "is" "isn't" "somewhat" "very" "extremely" "very very"@} for the fifth ## parameter. ## ## To run the demonstration code, type "@t{demo showrule}" (without the quotation ## marks) at the Octave prompt. ## ## @seealso{addrule, getfis, showfis} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy rule ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: showrule.m ## Last-Modified: 10 Jun 2024 function showrule (fis, index_list = [], format = 'verbose', ... language = 'english', ... verbose_strings = {"and" "or" "If" "then" "is" ... "isn't" "somewhat" "very" ... "extremely" "very very"}) ##-------------------------------------------------------------------- ## If the caller did not supply between 1 and 5 arguments with the ## correct types, print an error message and halt. ##-------------------------------------------------------------------- if (!(nargin >= 1 && nargin <= 5)) error ("showrule requires between 1 and 5 arguments\n"); elseif (!is_fis (fis)) error ("showrule's first argument must be an FIS structure\n"); elseif ((nargin >= 2) && ... !is_rule_index_list (index_list, length (fis.rule))) error ("showrule's second arg must be a vector of rule indices\n"); elseif ((nargin >= 3) && !is_format (format)) error ("showrule's third argument must specify the format\n"); elseif ((nargin == 4) && isequal (tolower (language), "custom")) error ("showrule: specify custom verbose strings in the fifth arg\n"); elseif ((nargin == 4) && !is_builtin_language (language)) error ("showrule's fourth arg must specify a built-in language\n"); elseif ((nargin == 5) && !isequal (tolower (language), "custom")) error ("showrule: use 'custom' as 4th arg to specify custom strings\n"); endif ##-------------------------------------------------------------------- ## If showrule was called with only one argument, create the default ## index list (all rule indices, in ascending order). ##-------------------------------------------------------------------- if (nargin == 1) index_list = 1 : length (fis.rule); endif ##-------------------------------------------------------------------- ## Show the rules in indexed, symbolic, or verbose format. ##-------------------------------------------------------------------- switch (tolower (format)) case 'indexed' showrule_indexed_format (fis, index_list); case 'symbolic' showrule_symbolic_format (fis, index_list); case 'verbose' showrule_verbose_format (fis, index_list, language, ... verbose_strings); endswitch endfunction ##---------------------------------------------------------------------- ## Function: get_verbose_hedge ## Purpose: For no hedge, return the empty string. ## For the built-in hedges, return the verbose string in the ## language used in the cell array verbose_strings (the second ## parameter). For custom hedges, return the power (rounded to ## two digits) to which the membership function matching value ## will be raised. ##---------------------------------------------------------------------- function hedge = get_verbose_hedge (mf_index_and_hedge, verbose_strings) mf_index_and_hedge = abs (mf_index_and_hedge); mf_index = fix (mf_index_and_hedge); hedge_num = round (100 * (mf_index_and_hedge - mf_index)); switch (hedge_num) case 0 ## .00 <=> no hedge <=> mu(x) hedge = ""; case 5 ## .05 <=> somewhat x <=> mu(x)^0.5 hedge = verbose_strings{7}; case 20 ## .20 <=> very x <=> mu(x)^2 hedge = verbose_strings{8}; case 30 ## .30 <=> extremely x <=> mu(x)^3 hedge = verbose_strings{9}; case 40 ## .40 <=> very very x <=> mu(x)^4 hedge = verbose_strings{10}; otherwise ## For custom hedge, return the hedge = hedge_num / 10; ## power dd/10. That is: endswitch ## .dd <=> x ## <=> mu(x)^(dd/10) endfunction ##---------------------------------------------------------------------- ## Function: get_is_or_isnt ## Purpose: Return the verbose string for "is" or "isn't" for the given ## membership function value. If the membership function value ## is 0, return the empty string. ##---------------------------------------------------------------------- function is_or_isnt = get_is_or_isnt (mem_fcn_value, verbose_strings) if (mem_fcn_value > 0) is_or_isnt = verbose_strings{5}; elseif (mem_fcn_value < 0) is_or_isnt = verbose_strings{6}; else is_or_isnt = ""; endif endfunction ##---------------------------------------------------------------------- ## Function: get_mf_name ## Purpose: Return the specified membership function name. ##---------------------------------------------------------------------- function mf_name = get_mf_name (mem_fcn_value, fis_input_or_output) mf_name = fis_input_or_output.mf(abs(fix(mem_fcn_value))).name; endfunction ##---------------------------------------------------------------------- ## Function: get_verbose_strings ## Purpose: Return a cell array of ten strings corresponding to: ## {"and" "or" "If" "then" "is" "isn't" ... ## "somewhat" "very" "extremely" "very very"} ## for the (built-in) language specified by the argument. ## Custom verbose strings are specified by an argument to ## showrule -- they are not handled by this function. ##---------------------------------------------------------------------- function str = get_verbose_strings (language) switch (language) case 'english' str = {"and" "or" "If" "then" "is" "isn't" ... "somewhat" "very" "extremely" "very very"}; case {'chinese' 'mandarin' 'pinyin'} str = {"he" "huo" "Ruguo" "name" "shi" "bu shi" ... "youdian" "hen" "feichang" "feichang feichang"}; case {'russian' 'russkij' 'pycckii'} str = {"i" "ili" "ecli" "togda" "" "ne" ... "nemnogo" "ochen" "prevoshodnoye" "ochen ochen"}; case {'spanish' 'espanol'} str = {"y" "o" "Si" "entonces" "es" "no es" ... "un poco" "muy" "extremadamente" "muy muy"}; case {'francais' 'french'} str = {"et" "ou" "Si" "alors" "est" "n'est pas" ... "un peu" "tres" "extremement" "tres tres"}; case {'deutsch' 'german'} str = {"und" "oder" "Wenn" "dann" "ist" "ist nicht" ... "ein wenig" "sehr" "auBerst" "sehr sehr"}; endswitch endfunction ##---------------------------------------------------------------------- ## Function: showrule_indexed_format ## Purpose: Show the rules in indexed format. ##---------------------------------------------------------------------- function showrule_indexed_format (fis, index_list) num_inputs = columns (fis.input); num_outputs = columns (fis.output); for i = 1 : length (index_list) current_ant = fis.rule(index_list(i)).antecedent; current_con = fis.rule(index_list(i)).consequent; current_wt = fis.rule(index_list(i)).weight; current_connect = fis.rule(index_list(i)).connection; ##------------------------------------------------------------------ ## Print membership functions for the inputs. ##------------------------------------------------------------------ for j = 1 : num_inputs if (is_int (current_ant(j))) printf ("%d", current_ant(j)); else printf ("%.2f", current_ant(j)); endif if (j == num_inputs) puts (","); endif puts (" "); endfor ##------------------------------------------------------------------ ## Print membership functions for the outputs. ##------------------------------------------------------------------ for j = 1 : num_outputs if (is_int (current_con(j))) printf ("%d", current_con(j)); else printf ("%.2f", current_con(j)); endif if (j < num_outputs) puts (" "); endif endfor ##------------------------------------------------------------------ ## Print the weight in parens. ##------------------------------------------------------------------ if (is_int (current_wt)) printf (" (%d) : ", current_wt); else printf (" (%.4f) : ", current_wt); endif ##------------------------------------------------------------------ ## Print the connection and a newline. ##------------------------------------------------------------------ printf ("%d\n", current_connect); endfor endfunction ##---------------------------------------------------------------------- ## Function: showrule_symbolic_format ## Purpose: Show the rules in symbolic format. ##---------------------------------------------------------------------- function showrule_symbolic_format (fis, index_list) verbose_strings = {"&&" "||" "" "=>" "==" "!=" ... 0.5 2.0 3.0 4.0}; showrule_verbose_format (fis, index_list, "custom", ... verbose_strings, true); endfunction ##---------------------------------------------------------------------- ## Function: showrule_verbose_format ## Purpose: Show the rules in verbose format. ##---------------------------------------------------------------------- function showrule_verbose_format (fis, index_list, language, ... verbose_strings, ... suppress_comma = false) num_inputs = columns (fis.input); num_outputs = columns (fis.output); ##-------------------------------------------------------------------- ## Get verbose strings in the (built-in) language specified. Note ## that the strings for custom languages are supplied by the user. ##-------------------------------------------------------------------- language = tolower (language); if (isequal ("custom", language)) str = verbose_strings; else str = get_verbose_strings (language); endif and_str = str{1}; if_str = str{3}; then_str = str{4}; ##-------------------------------------------------------------------- ## For each index in the index_list, print the index number, the rule, ## and the weight. ##-------------------------------------------------------------------- for i = 1 : length (index_list) connect_str = str{fis.rule(index_list(i)).connection}; current_ant = fis.rule(index_list(i)).antecedent; current_con = fis.rule(index_list(i)).consequent; current_wt = fis.rule(index_list(i)).weight; ##------------------------------------------------------------------ ## For j = 1, print: ## . If ( [] ) ## and for 2 <= j <= num_inputs, print: ## ( [] ) ## in the specified language. Custom hedges are printed in the form: ## ( ^) ##------------------------------------------------------------------ first_input_printed = true; for j = 1 : num_inputs if (j == 1) printf ("%d.", index_list(i)); endif input_name = fis.input(j).name; is_or_isnt = get_is_or_isnt (current_ant(j), str); if (!isempty (is_or_isnt)) hedge = get_verbose_hedge (current_ant(j), str); mf_name = get_mf_name (current_ant(j), fis.input(j)); if (first_input_printed) first_input_printed = false; printf (" %s", if_str); else printf (" %s", connect_str); endif if (isempty (hedge)) printf (" (%s %s %s)", input_name, is_or_isnt, mf_name); elseif (ischar (hedge)) printf (" (%s %s %s %s)", input_name, is_or_isnt, hedge, ... mf_name); else printf (" (%s %s %s^%3.1f)", input_name, is_or_isnt, ... mf_name, hedge); endif endif endfor ##------------------------------------------------------------------ ## Print the consequent in the form: ## ", then (output-name is [hedge] mem-fcn-name) and ## (output-name is [hedge] mem-fcn-name) and ## ... ## (output-name is [hedge] mem-fcn-name)" ## ## Only the outputs for which the membership function index is ## non-zero are printed. Negative membership function indices ## indicate "isn't" instead of "is", and the fractional part of ## the membership function index indicates a hedge, which is also ## printed. ## ## For non-numeric and empty hedges, print each of the outputs ## using the form: ## ( [] ) ## For custom and numeric hedges, use the form: ## ( ^) ## ## The comma may be suppressed (as it is for symbolic output) by ## calling the function with suppress_comma == true. ##------------------------------------------------------------------ first_output_printed = true; for j = 1 : num_outputs output_name = fis.output(j).name; is_or_isnt = get_is_or_isnt (current_con(j), str); if (!isempty (is_or_isnt)) hedge = get_verbose_hedge (current_con(j), str); mf_name = get_mf_name (current_con(j), fis.output(j)); if (first_output_printed) first_output_printed = false; if (suppress_comma) printf (" %s", then_str); else printf (", %s", then_str); endif else printf (" %s", and_str); endif if (isempty (hedge)) printf (" (%s %s %s)", output_name, is_or_isnt, mf_name); elseif (ischar (hedge)) printf (" (%s %s %s %s)", output_name, is_or_isnt, hedge, ... mf_name); else printf (" (%s %s %s^%3.1f)", output_name, is_or_isnt, ... mf_name, hedge); endif endif endfor ##------------------------------------------------------------------ ## Finally, print the weight in parens and a newline: ## " ()" ##------------------------------------------------------------------ if is_int (current_wt) printf (" (%d)\n", current_wt); else printf (" (%.4f)\n", current_wt); endif endfor endfunction ##---------------------------------------------------------------------- ## Embedded Demos and Tests ##---------------------------------------------------------------------- %!demo %! fis = readfis ('sugeno_tip_calculator.fis'); %! puts ("Output of: showrule(fis)\n"); %! showrule (fis) %! puts ("\n"); %!demo %! fis = readfis ('sugeno_tip_calculator.fis'); %! puts ("Output of: showrule(fis, [2 4], 'symbolic')\n"); %! showrule (fis, [2 4], 'symbolic') %! puts ("\n"); %!demo %! fis = readfis ('sugeno_tip_calculator.fis'); %! puts ("Output of: showrule(fis, 1:4, 'indexed')\n"); %! showrule (fis, 1:4, 'indexed') %! puts ("\n"); %!demo %! fis = readfis ('sugeno_tip_calculator.fis'); %! puts ("Output of: showrule(fis, 1, 'verbose', 'francais')\n"); %! showrule (fis, 1, 'verbose', 'francais') %! puts ("\n"); %!shared fis %! fis = readfis ('mamdani_tip_calculator.fis'); ## Test input validation %!error %! showrule() %!error %! showrule(1, 2, 3, 4, 5, 6) %!error %! showrule(1, 2, 3, 4, 5) %!error %! showrule(fis, '2', 3, 4, 5) %!error %! showrule(fis, 2, 3, 4, 5) %!error %! showrule(fis, [2 4], 'verbose', 'custom') %!error %! showrule(fis, [2 4], 'verbose', 4) %!error %! showrule(fis, [2 4], 'verbose', 'english', 5) fuzzy-logic-toolkit-0.6.1/inst/sigmf.m000066400000000000000000000102701466512601400177300ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} sigmf (@var{x}, @var{params}) ## @deftypefnx {Function File} {@var{y} =} sigmf (@var{[x1 x2 ... xn]}, @var{[a c]}) ## ## For a given domain @var{x} and parameters @var{params} (or @var{[a c]}), ## return the corresponding @var{y} values for the sigmoidal membership ## function. ## ## The argument @var{x} must be a real number or a non-empty vector of strictly ## increasing real numbers, and @var{a} and @var{c} must be real numbers. This ## membership function satisfies the equation: ## ## @verbatim ## f(x) = 1/(1 + exp(-a*(x - c))) ## @end verbatim ## ## which always returns values in the range [0, 1]. ## ## The parameters a and c specify: ## ## @verbatim ## a == the slope at c ## c == the inflection point ## @end verbatim ## ## and at the inflection point, the value of the function is 0.5: ## ## @verbatim ## f(c) == 0.5. ## @end verbatim ## ## To run the demonstration code, type "@t{demo sigmf}" (without the quotation ## marks) at the Octave prompt. ## ## @seealso{dsigmf, gauss2mf, gaussmf, gbellmf, pimf, psigmf, smf, trapmf, trimf, zmf} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy membership sigmoidal ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: sigmf.m ## Last-Modified: 13 Jun 2024 function y = sigmf (x, params) ## If the caller did not supply 2 argument values with the correct ## types, print an error message and halt. if (nargin != 2) error ("sigmf requires 2 arguments\n"); elseif (!is_domain (x)) error ("sigmf's first argument must be a valid domain\n"); elseif (!are_mf_params ('sigmf', params)) error ("sigmf's second argument must be a parameter vector\n"); endif ## Calculate and return the y values of the membership function on the ## domain x. a = params(1); c = params(2); y_val = @(x_val) 1 / (1 + exp (-a * (x_val - c))); y = arrayfun (y_val, x); endfunction %!demo %! x = 0:100; %! params = [0.3 40]; %! y1 = sigmf(x, params); %! params = [0.2 40]; %! y2 = sigmf(x, params); %! params = [0.1 40]; %! y3 = sigmf(x, params); %! figure('NumberTitle', 'off', 'Name', 'sigmf demo'); %! plot(x, y1, 'r;params = [0.3 40];', 'LineWidth', 2) %! hold on; %! plot(x, y2, 'b;params = [0.2 40];', 'LineWidth', 2) %! hold on; %! plot(x, y3, 'g;params = [0.1 40];', 'LineWidth', 2) %! ylim([-0.1 1.2]); %! xlabel('Crisp Input Value', 'FontWeight', 'bold'); %! ylabel('Degree of Membership', 'FontWeight', 'bold'); %! grid; %!test %! x = 0:10; %! params = [5 2]; %! y = [4.5398e-05 6.6929e-03 0.5000 0.9933 1 1 1 1 1 1 1]; %! z = sigmf(x, params); %! assert(z, y, 1e-4); ## Test input validation %!error %! sigmf() %!error %! sigmf(1) %!error %! sigmf(1, 2, 3) %!error %! sigmf([1 0], 2) %!error %! sigmf(1, 2) %!error %! sigmf(0:100, []) %!error %! sigmf(0:100, [30]) %!error %! sigmf(0:100, [90 80 30]) %!error %! sigmf(0:100, 'abc') %!error %! sigmf(0:100, '') fuzzy-logic-toolkit-0.6.1/inst/smf.m000066400000000000000000000125461466512601400174200ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} smf (@var{x}, @var{params}) ## @deftypefnx {Function File} {@var{y} =} smf (@var{[x1 x2 ... xn]}, @var{[a b]}) ## ## For a given domain @var{x} and parameters @var{params} (or @var{[a b]}), ## return the corresponding @var{y} values for the S-shaped membership function. ## ## The argument @var{x} must be a real number or a non-empty vector of strictly ## increasing real numbers, and @var{a} and @var{b} must be real numbers, with ## @var{a} < @var{b}. This membership function satisfies: ## ## @verbatim ## 0 if x <= a ## f(x) = 2 * ((x - a)/(b - a))^2 if a < x <= (a + b)/2 ## 1 - 2 * ((x - b)/(b - a))^2 if (a + b)/2 < x < b ## 1 if x >= b ## @end verbatim ## ## which always returns values in the range [0, 1]. ## ## To run the demonstration code, type "@t{demo smf}" (without the quotation ## marks) at the Octave prompt. ## ## @seealso{dsigmf, gauss2mf, gaussmf, gbellmf, pimf, psigmf, sigmf, trapmf, trimf, zmf} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy membership s-shaped ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: smf.m ## Last-Modified: 13 Jun 2024 function y = smf (x, params) ## If the caller did not supply 2 argument values with the correct ## types, print an error message and halt. if (nargin != 2) error ("smf requires 2 arguments\n"); elseif (!is_domain (x)) error ("smf's first argument must be a valid domain\n"); elseif (!are_mf_params ('smf', params)) error ("smf's second argument must be a parameter vector\n"); endif ## Calculate and return the y values of the membership function on the ## domain x. a = params(1); b = params(2); a_b_ave = (a + b) / 2; b_minus_a = b - a; y_val = @(x_val) smf_val (x_val, a, b, a_b_ave, b_minus_a); y = arrayfun (y_val, x); endfunction ##---------------------------------------------------------------------- ## Usage: y = smf_val (x_val, a, b, a_b_ave, b_minus_a) ## ## smf_val returns one value of the S-shaped membership function, which ## satisfies: ## 0 if x <= a ## f(x) = 2 * ((x - a)/(b - a))^2 if a < x <= (a + b)/2 ## 1 - 2 * ((x - b)/(b - a))^2 if (a + b)/2 < x < b ## 1 if x >= b ## ## smf_val is a private function, called only by smf. Because smf_val ## is not intended for general use -- and because the parameters a and b ## are checked for errors in the function smf (defined above), the ## parameters are not checked for errors again here. ##---------------------------------------------------------------------- function y_val = smf_val (x_val, a, b, a_b_ave, b_minus_a) ## Calculate and return a single y value of the S-shaped membership ## function for the given x value and parameters specified by the ## arguments. if (x_val <= a) y_val = 0; elseif (x_val <= a_b_ave) y_val = 2 * ((x_val - a) / b_minus_a)^2; elseif (x_val < b) y_val = 1 - 2 * ((x_val - b) / b_minus_a)^2; else y_val = 1; endif endfunction %!demo %! x = 0:100; %! params = [40 60]; %! y1 = smf(x, params); %! params = [25 75]; %! y2 = smf(x, params); %! params = [10 90]; %! y3 = smf(x, params); %! figure('NumberTitle', 'off', 'Name', 'smf demo'); %! plot(x, y1, 'r;params = [40 60];', 'LineWidth', 2) %! hold on; %! plot(x, y2, 'b;params = [25 75];', 'LineWidth', 2) %! hold on; %! plot(x, y3, 'g;params = [10 90];', 'LineWidth', 2) %! ylim([-0.1 1.2]); %! xlabel('Crisp Input Value', 'FontWeight', 'bold'); %! ylabel('Degree of Membership', 'FontWeight', 'bold'); %! grid; %!test %! x = 0:10:100; %! params = [25 75]; %! y = [0 0 0 0.020000 0.1800 0.5000 0.8200 0.9800 1 1 1]; %! z = smf(x, params); %! assert(z, y, 1e-4); ## Test input validation %!error %! smf() %!error %! smf(1) %!error %! smf(1, 2, 3) %!error %! smf([1 0], 2) %!error %! smf(1, 2) %!error %! smf(0:100, []) %!error %! smf(0:100, [30]) %!error %! smf(0:100, [90 80 30]) %!error %! smf(0:100, 'abc') %!error %! smf(0:100, '') fuzzy-logic-toolkit-0.6.1/inst/sugeno_tip_calculator.fis000066400000000000000000000047751466512601400235520ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fis ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: sugeno_tip_calculator.fis ## Last-Modified: 28 Aug 2012 % Sugeno Tip Calculator % Computes cheap, average, and generous tips % given food quality and service ratings. [System] Name = 'Sugeno-Tip-Calculator' Type = 'sugeno' Version = 1.0 NumInputs = 2 NumOutputs = 3 NumRules = 10 AndMethod = 'einstein_product' OrMethod = 'einstein_sum' ImpMethod = 'prod' AggMethod = 'sum' DefuzzMethod = 'wtaver' [Input1] Name = 'Food-Quality' Range = [1 10] NumMFs = 2 MF1 = 'Bad' : 'trapmf', [0 1 3 7] MF2 = 'Good' : 'trapmf', [3 7 10 11] [Input2] Name = 'Service' Range = [1 10] NumMFs = 2 MF1 = 'Bad' : 'trapmf', [0 1 3 7] MF2 = 'Good' : 'trapmf', [3 7 10 11] [Output1] Name = 'Cheap-Tip' Range = [5 25] NumMFs = 3 MF1 = 'Low' : 'constant', [10] MF2 = 'Medium' : 'constant', [15] MF3 = 'High' : 'constant', [20] [Output2] Name = 'Average-Tip' Range = [5 25] NumMFs = 3 MF1 = 'Low' : 'constant', [10] MF2 = 'Medium' : 'constant', [15] MF3 = 'High' : 'constant', [20] [Output3] Name = 'Generous-Tip' Range = [5 25] NumMFs = 3 MF1 = 'Low' : 'constant', [10] MF2 = 'Medium' : 'constant', [15] MF3 = 'High' : 'constant', [20] [Rules] 1.30 1.30, 1.30 1.20 1.00 (1) : 1 2.00 1.30, 1.00 1.00 2.00 (1) : 1 2.20 1.20, 1.00 2.00 3.00 (1) : 1 1.00 1.00, 1.00 1.00 2.00 (1) : 1 2.00 1.00, 1.00 2.00 3.00 (1) : 1 2.30 1.00, 1.00 2.00 3.20 (1) : 1 1.00 2.00, 1.00 2.00 3.00 (1) : 1 2.00 2.00, 2.00 2.00 3.20 (1) : 1 1.20 2.20, 1.00 2.00 3.00 (1) : 1 2.40 2.40, 3.00 3.20 3.30 (1) : 1 fuzzy-logic-toolkit-0.6.1/inst/sugeno_tip_demo.m000066400000000000000000000062311466512601400220050ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Script File} {} sugeno_tip_demo ## ## Demonstrate the use of the Octave Fuzzy Logic Toolkit to read and ## evaluate a Sugeno-type FIS with multiple outputs stored in a text ## file. Also demonstrate the use of hedges in the FIS rules and the ## Einstein product and sum as the T-norm/S-norm pair. ## ## The demo: ## @itemize @bullet ## @item ## reads the FIS structure from a file ## @item ## plots the input membership functions ## @item ## plots the (constant) output functions ## @item ## plots each of the three FIS outputs as a function of the inputs ## @item ## displays the FIS rules in verbose format in the Octave window ## @item ## evaluates the Sugeno-type FIS for six inputs ## @end itemize ## ## @seealso{cubic_approx_demo, heart_disease_demo_1, heart_disease_demo_2, investment_portfolio_demo, linear_tip_demo, mamdani_tip_demo} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy tests demos ## Note: This example is based on an assignment written by ## Dr. Bruce Segee (University of Maine Dept. of ECE). ## Directory: fuzzy-logic-toolkit/inst ## Filename: sugeno_tip_demo.m ## Last-Modified: 4 Jun 2024 ## Read the FIS structure from a file. fis = readfis ('sugeno_tip_calculator.fis'); ## Plot the input and output membership functions. plotmf (fis, 'input', 1); plotmf (fis, 'input', 2); plotmf (fis, 'output', 1); plotmf (fis, 'output', 2); plotmf (fis, 'output', 3); ## Plot the cheap, average, and generous tips as a function of ## Food-Quality and Service. gensurf (fis, [1 2], 1); gensurf (fis, [1 2], 2); gensurf (fis, [1 2], 3); ## Demonstrate showrule with hedges. showrule (fis); ## Calculate the Tip for 6 sets of input values: puts ("\nFor the following values of (Food Quality, Service):\n\n"); food_service = [1 1; 5 5; 10 10; 4 6; 6 4; 7 4] puts ("\nThe cheap, average, and generous tips are:\n\n"); tip = evalfis (food_service, fis, 1001) %!test %! fis = readfis ('sugeno_tip_calculator.fis'); %! food_service = [1 1; 5 5; 10 10; 4 6; 6 4; 7 4]; %! tip = evalfis (food_service, fis, 1001); %! expected_result = ... %! [10.000 10.000 12.500 %! 10.868 13.681 19.138 %! 17.500 17.500 20.000 %! 10.604 14.208 19.452 %! 10.427 13.687 19.033 %! 10.471 14.358 19.353]; %! assert(tip, expected_result, 1e-3); fuzzy-logic-toolkit-0.6.1/inst/trapmf.m000066400000000000000000000113371466512601400201210ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} trapmf (@var{x}, @var{params}) ## @deftypefnx {Function File} {@var{y} =} trapmf (@var{[x1 x2 ... xn]}, @var{[a b c d]}) ## ## For a given domain @var{x} and parameters @var{params} (or @var{[a b c d]}), ## return the corresponding @var{y} values for the trapezoidal membership ## function. ## ## The argument @var{x} must be a real number or a non-empty vector of ## strictly increasing real numbers, and parameters @var{a}, @var{b}, @var{c}, ## and @var{d} must satisfy the inequalities: ## @var{a} < @var{b} <= @var{c} < @var{d}. None of the parameters @var{a}, ## @var{b}, @var{c}, @var{d} are required to be in the domain @var{x}. The ## minimum and maximum values of the trapezoid are assumed to be 0 and 1. ## ## The parameters @var{[a b c d]} correspond to the x values ## of the corners of the trapezoid: ## ## @verbatim ## 1-| -------- ## | / \ ## | / \ ## | / \ ## 0----------------------- ## a b c d ## @end verbatim ## ## To run the demonstration code, type "@t{demo trapmf}" (without the quotation ## marks) at the Octave prompt. ## ## @seealso{dsigmf, gauss2mf, gaussmf, gbellmf, pimf, psigmf, sigmf, smf, trimf, zmf} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy membership trapezoidal ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: trapmf.m ## Last-Modified: 13 Jun 2024 function y = trapmf (x, params) ## If the caller did not supply 2 argument values with the correct ## types, print an error message and halt. if (nargin != 2) error ("trapmf requires 2 arguments\n"); elseif (!is_domain (x)) error ("trapmf's first argument must be a valid domain\n"); elseif (!are_mf_params ('trapmf', params)) error ("trapmf's second argument must be a parameter vector\n"); endif ## Calculate and return the y values of the trapezoid on the domain x. a = params(1); b = params(2); c = params(3); d = params(4); b_minus_a = b - a; d_minus_c = d - c; y_val = @(x_val) max (0, min (min (1, (x_val - a) / b_minus_a), ... (d - x_val) / d_minus_c)); y = arrayfun (y_val, x); endfunction %!demo %! x = 0:100; %! params = [-1 0 20 40]; %! y1 = trapmf(x, params); %! params = [20 40 60 80]; %! y2 = trapmf(x, params); %! params = [60 80 100 101]; %! y3 = trapmf(x, params); %! figure('NumberTitle', 'off', 'Name', 'trapmf demo'); %! plot(x, y1, 'r;params = [-1 0 20 40];', 'LineWidth', 2) %! hold on; %! plot(x, y2, 'b;params = [20 40 60 80];', 'LineWidth', 2) %! hold on; %! plot(x, y3, 'g;params = [60 80 100 101];', 'LineWidth', 2) %! ylim([-0.1 1.2]); %! xlabel('Crisp Input Value', 'FontWeight', 'bold'); %! ylabel('Degree of Membership', 'FontWeight', 'bold'); %! grid; %!test %! x = 0:10; %! params = [-1 0 2 4]; %! y1 = trapmf(x, params); %! assert(y1, [1.0 1.0 1.0 0.5 0 0 0 0 0 0 0]); %! params = [2 4 6 8]; %! y2 = trapmf(x, params); %! assert(y2, [0 0 0 0.5 1.0 1.0 1.0 0.5 0 0 0]); %! params = [6 8 10 11]; %! y3 = trapmf(x, params); %! assert(y3, [0 0 0 0 0 0 0 0.5 1.0 1.0 1.0]); ## Test input validation %!error %! trapmf() %!error %! trapmf(1) %!error %! trapmf(1, 2, 3) %!error %! trapmf([1 0], 2) %!error %! trapmf(1, 2) %!error %! trapmf(0:100, []) %!error %! trapmf(0:100, [2]) %!error %! trapmf(0:100, [2 3]) %!error %! trapmf(0:100, [90 80 30 20]) %!error %! trapmf(0:100, [30 80 20 20]) fuzzy-logic-toolkit-0.6.1/inst/trimf.m000066400000000000000000000111461466512601400177470ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} trimf (@var{x}, @var{params}) ## @deftypefnx {Function File} {@var{y} =} trimf (@var{[x1 x2 ... xn]}, @var{[a b c]}) ## ## For a given domain @var{x} and parameters @var{params} (or @var{[a b c]}), ## return the corresponding @var{y} values for the triangular membership ## function. ## ## The argument @var{x} must be a real number or a non-empty vector of strictly ## increasing real numbers, and parameters @var{a}, @var{b}, and @var{c} must be ## real numbers that satisfy @var{a} < @var{b} < @var{c}. None of the parameters ## @var{a}, @var{b}, and @var{c} are required to be in the domain @var{x}. The ## minimum and maximum values of the triangle are assumed to be 0 and 1. ## ## The parameters [@var{a} @var{b} @var{c}] correspond to the x values of the ## vertices of the triangle: ## ## @verbatim ## 1-| /\ ## | / \ ## | / \ ## | / \ ## 0----------------------- ## a b c ## @end verbatim ## ## To run the demonstration code, type "@t{demo trimf}" (without the quotation ## marks) at the Octave prompt. ## ## @seealso{dsigmf, gauss2mf, gaussmf, gbellmf, pimf, psigmf, sigmf, smf, trapmf, trimf_demo, zmf} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy membership triangular ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: trimf.m ## Last-Modified: 13 Jun 2024 function y = trimf (x, params) ## If the caller did not supply 2 argument values with the correct ## types, print an error message and halt. if (nargin != 2) error ("trimf requires 2 arguments\n"); elseif (!is_domain (x)) error ("trimf's first argument must be a valid domain\n"); elseif (!are_mf_params ('trimf', params)) error ("trimf's second argument must be a parameter vector\n"); endif ## Calculate and return the y values of the triangle on the domain x. a = params(1); b = params(2); c = params(3); b_minus_a = b - a; c_minus_b = c - b; y_val = @(x_val) max (0, min (min (1, (x_val - a) / b_minus_a), ... (c - x_val)/c_minus_b)); y = arrayfun (y_val, x); endfunction %!demo %! x = 0:100; %! params = [-1 0 50]; %! y1 = trimf(x, params); %! params = [0 50 100]; %! y2 = trimf(x, params); %! params = [50 100 101]; %! y3 = trimf(x, params); %! figure('NumberTitle', 'off', 'Name', 'trimf demo'); %! plot(x, y1, 'r;params = [-1 0 50];', 'LineWidth', 2) %! hold on; %! plot(x, y2, 'b;params = [0 50 100];', 'LineWidth', 2) %! hold on; %! plot(x, y3, 'g;params = [50 100 101];', 'LineWidth', 2) %! ylim([-0.1 1.2]); %! xlabel('Crisp Input Value', 'FontWeight', 'bold'); %! ylabel('Degree of Membership', 'FontWeight', 'bold'); %! grid; %!test %! x = 0:10; %! params = [0 2 4]; %! y1 = trimf(x, params); %! assert(y1, [0 0.5 1.0 0.5 0 0 0 0 0 0 0]); %! params = [2 4 6]; %! y2 = trimf(x, params); %! assert(y2, [0 0 0 0.5 1.0 0.5 0 0 0 0 0]); %! params = [6 8 10]; %! y3 = trimf(x, params); %! assert(y3, [0 0 0 0 0 0 0 0.5 1.0 0.5 0]); ## Test input validation %!error %! trimf() %!error %! trimf(1) %!error %! trimf(1, 2, 3) %!error %! trimf([1 0], 2) %!error %! trimf(1, 2) %!error %! trimf(0:100, []) %!error %! trimf(0:100, [2]) %!error %! trimf(0:100, [2 3]) %!error %! trimf(0:100, [90 80 30]) %!error %! trimf(0:100, [30 80 20]) fuzzy-logic-toolkit-0.6.1/inst/writefis.m000066400000000000000000000243551466512601400204700ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {} writefis (@var{fis}) ## @deftypefnx {Function File} {} writefis (@var{fis}, @var{filename}) ## @deftypefnx {Function File} {} writefis (@var{fis}, @var{filename}, @var{dialog}) ## ## Save the specified FIS currently in the Octave workspace to a file ## named by the user. ## ## There are three forms of writefis: ## ## @multitable @columnfractions .20 .70 ## @headitem Number of Arguments @tab Action Taken ## @item 1 ## @tab Open a dialog GUI to help the user choose a directory and name ## for the output file. ## @item 2 ## @tab Do not open a dialog GUI. Save the FIS to a file in the ## current directory with the specified @var{filename}. If the ## specified @var{filename} does not end in '.fis', append '.fis' ## to the @var{filename}. ## @item 3 ## @tab Open a dialog GUI with the specified @var{filename} in the ## 'filename' textbox of the GUI. If the specified @var{filename} ## does not end in '.fis', append '.fis' to the @var{filename}. ## @end multitable ## @sp 1 ## The types/values of the arguments are expected to be: ## ## @multitable @columnfractions .20 .70 ## @headitem Argument @tab Expected Type or Value ## @item @var{fis} ## @tab an FIS structure satisfying is_fis (see private/is_fis.m) ## @item @var{filename} ## @tab a string; if the string does not already end with the extension ## ".fis", then ".fis" is added ## @item @var{dialog} ## @tab the string 'dialog' (case insensitive) ## @end multitable ## @sp 1 ## Note: ## The GUI dialog requires zenity to be installed on the system. ## ## Known error: ## When using the file dialog, if the user clicks "Cancel" instead of ## saving the file, an error message is generated. ## ## @seealso{readfis} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy inference system fis ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: writefis.m ## Last-Modified: 13 Jun 2024 function writefis (fis, filename = 'filename.fis', dialog = 'dummy') ## If writefis was not called with between 1 and 3 arguments, or if ## the argument values were of the wrong type, print an error message ## and halt. if (!(nargin >= 1 && nargin <= 3)) error ("writefis requires between 1 and 3 arguments\n"); elseif (!is_fis (fis)) error ("writefis's first argument must be an FIS structure\n"); elseif ((nargin >= 2) && !is_string (filename)) error ("writefis's second argument must be a string\n"); elseif ((nargin == 3) && ... !(is_string (dialog) && strcmpi (dialog, 'dialog'))) error ("writefis's third argument must the string 'dialog'\n"); endif ## Open the output file. use_gui = (nargin != 2); fid = open_output_file (filename, use_gui); ## Write the [System], [Input], [Output], and [Rules] ## sections of the output file. write_system_section (fid, fis); write_input_sections (fid, fis); write_output_sections (fid, fis); write_rules_section (fid, fis); ## Close the output file. fclose (fid); endfunction ##---------------------------------------------------------------------- ## Function: open_output_file ## Purpose: Open the output file. Return the fid if successful. ## Otherwise, print an error message and halt. ##---------------------------------------------------------------------- function fid = open_output_file (filename, use_gui) ## If the filename is not empty, and if the last four characters of ## the filename are not '.fis', append '.fis' to the filename. fn_len = length (filename); if (((fn_len >= 4) && ... !strcmp(".fis",filename(fn_len-3:fn_len))) || ... ((fn_len > 0) && (fn_len < 4))) filename = [filename ".fis"]; endif ## If writefis was called with 1 or 3 arguments, use a dialog to ## choose an output filename. if (use_gui) system_command = sprintf ("zenity --file-selection --filename=%s \ --save --confirm-overwrite; \ echo $file", filename); [dialog_error, filename] = system (file=system_command); if (dialog_error) error ("error selecting file using dialog\n"); endif filename = strtrim (filename); endif ## Open output file. [fid, msg] = fopen (filename, "w"); if (fid == -1) if (use_gui) system ('zenity --error --text "Error opening output file."'); endif error ("error opening output file: %s\n", msg); endif endfunction ##---------------------------------------------------------------------- ## Function: write_system_section ## Purpose: Write [System] section of the output file. ##---------------------------------------------------------------------- function write_system_section (fid, fis) fprintf (fid, "[System]\n"); fprintf (fid, "Name='%s'\n", fis.name); fprintf (fid, "Type='%s'\n", fis.type); fprintf (fid, "Version=%.1f\n", fis.version); fprintf (fid, "NumInputs=%d\n", columns(fis.input)); fprintf (fid, "NumOutputs=%d\n", columns(fis.output)); fprintf (fid, "NumRules=%d\n", columns(fis.rule)); fprintf (fid, "AndMethod='%s'\n", fis.andMethod); fprintf (fid, "OrMethod='%s'\n", fis.orMethod); fprintf (fid, "ImpMethod='%s'\n", fis.impMethod); fprintf (fid, "AggMethod='%s'\n", fis.aggMethod); fprintf (fid, "DefuzzMethod='%s'\n", fis.defuzzMethod); endfunction ##---------------------------------------------------------------------- ## Function: write_input_sections ## Purpose: For each FIS input, write [Input] section to ## output file. ##---------------------------------------------------------------------- function write_input_sections (fid, fis) num_inputs = columns (fis.input); for i = 1 : num_inputs num_mfs = columns (fis.input(i).mf); fprintf (fid, "\n[Input%d]\n", i); fprintf (fid, "Name='%s'\n", fis.input(i).name); fprintf (fid, "Range=%s\n", ... strrep (mat2str (fis.input(i).range),","," ")); fprintf (fid, "NumMFs=%d\n", num_mfs); for j = 1 : num_mfs fprintf (fid, "MF%d='%s':'%s',%s\n", j, ... fis.input(i).mf(j).name, fis.input(i).mf(j).type, ... params2str (fis.input(i).mf(j).params)); endfor endfor endfunction ##---------------------------------------------------------------------- ## Function: write_output_sections ## Purpose: For each FIS output, write [Output] section to ## output file. ##---------------------------------------------------------------------- function write_output_sections (fid, fis) num_outputs = columns (fis.output); for i = 1 : num_outputs num_mfs = columns (fis.output(i).mf); fprintf (fid, "\n[Output%d]\n", i); fprintf (fid, "Name='%s'\n", fis.output(i).name); fprintf (fid, "Range=%s\n", ... strrep(mat2str(fis.output(i).range),","," ")); fprintf (fid, "NumMFs=%d\n", num_mfs); for j = 1 : num_mfs fprintf (fid, "MF%d='%s':'%s',%s\n", j, ... fis.output(i).mf(j).name, fis.output(i).mf(j).type, ... params2str (fis.output(i).mf(j).params)); endfor endfor endfunction ##---------------------------------------------------------------------- ## Function: write_rules_section ## Purpose: Write [Rules] section to output file. ##---------------------------------------------------------------------- function write_rules_section (fid, fis) num_inputs = columns (fis.input); num_outputs = columns (fis.output); num_rules = columns (fis.rule); fprintf (fid, "\n[Rules]\n"); for i = 1 : num_rules next_ant = fis.rule(i).antecedent; next_con = fis.rule(i).consequent; next_wt = fis.rule(i).weight; next_connect = fis.rule(i).connection; ## Print membership functions for the inputs. if (num_inputs > 0) if (is_int (next_ant(1))) fprintf (fid, "%d", next_ant(1)); else fprintf (fid, "%.2f", next_ant(1)); endif endif for j = 2 : num_inputs if (is_int (next_ant(j))) fprintf (fid, " %d", next_ant(j)); else fprintf (fid, " %.2f", next_ant(j)); endif endfor fprintf(fid, ", "); ## Print membership functions for the outputs. for j = 1 : num_outputs if (is_int (next_con(j))) fprintf (fid, "%d ", next_con(j)); else fprintf (fid, "%.2f ", next_con(j)); endif endfor ## Print the weight in parens. if (is_int (next_wt)) fprintf (fid, "(%d) : ", next_wt); else fprintf (fid, "(%.4f) : ", next_wt); endif ## Print the connection and a newline. fprintf (fid, "%d\n", next_connect); endfor endfunction ##---------------------------------------------------------------------- ## Function: params2str ## Purpose: Convert membership function parameters to string ## representation. ##---------------------------------------------------------------------- function str = params2str (params) if (length (params) < 2) str = ['[' num2str(params) ']']; else str = strrep (mat2str (params), ",", " "); endif endfunction %!shared fis %! fis = readfis ('sugeno_tip_calculator.fis'); ## Test input validation %!error %! writefis() %!error %! writefis(1) %!error %! writefis(fis, 2) %!error %! writefis(fis, 'temp.fis', 'abc') %!error %! writefis(1, 2, 3, 4) fuzzy-logic-toolkit-0.6.1/inst/xie_beni_index.m000066400000000000000000000121331466512601400215740ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{vxb} =} xie_beni_index (@var{input_data}, @var{cluster_centers}, @var{soft_partition}) ## ## Return the Xie-Beni validity index for a given soft partition. ## ## The arguments to xie_beni_index are: ## @itemize @w ## @item ## @var{input_data}: a matrix of input data points; each row corresponds to one point ## @item ## @var{cluster_centers}: a matrix of cluster centers; each row corresponds to one point ## @item ## @var{soft_partition}: the membership degree of each input data point in each cluster ## @end itemize ## ## The return value is: ## @itemize @w ## @item ## @var{vxb}: the Xie-Beni validity index for the given partition ## @end itemize ## ## To run demonstration code that uses this function, type "@t{demo fcm}" ## or "@t{demo gustafson_kessel}" (without the quotation marks) at the ## Octave prompt. ## ## For more information about the @var{input_data}, @var{cluster_centers}, ## and @var{soft_partition} matrices, please see the documentation for function ## fcm. ## ## @seealso{fcm, gustafson_kessel, partition_coeff, partition_entropy} ## ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy xie beni cluster validity ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: xie_beni_index.m ## Last-Modified: 13 Jun 2024 function vxb = xie_beni_index (input_data, cluster_centers, ... soft_partition) ## If xie_beni_index was called with an incorrect number of arguments, ## or the argument does not have the correct type, print an error ## message and halt. if (nargin != 3) error ("xie_beni_index requires 3 arguments\n"); elseif (!is_real_matrix (input_data)) error ("xie_beni_index's first argument must be matrix of reals\n"); elseif (!(is_real_matrix (cluster_centers) && (columns (cluster_centers) == columns (input_data)))) error ("xie_beni_index's 2nd arg must be matrix of reals with same #cols as input_data\n"); elseif (!(is_real_matrix (soft_partition) && (min (min (soft_partition)) >= 0) && (max (max (soft_partition)) <= 1))) error ("xie_beni_index's 3rd arg must be a matrix of reals 0.0-1.0\n"); endif ## Compute and return the Xie-Beni index. vxb = xie_beni_private (input_data, cluster_centers, soft_partition); endfunction ##---------------------------------------------------------------------- ## Function: xie_beni_private ## Purpose: Return the Xie-Beni index for the given soft partition. ## Note: The following is an implementation of Equations 13.11, ## 13.12, and 13.13 in Fuzzy Logic: Intelligence, Control and ## Information, by J. Yen and R. Langari, Prentice Hall, 1999, ## page 384 (International Edition). ##---------------------------------------------------------------------- function vxb = xie_beni_private (X, V, Mu) sqr_dist = square_distance_matrix (X, V); sum_sigma = sum (sum (Mu .* sqr_dist)); n = rows (X); d_sqr_min = min_sqr_dist_between_centers (V); vxb = sum_sigma / (n * d_sqr_min); endfunction ##---------------------------------------------------------------------- ## Function: min_sqr_dist_between_centers ## Purpose: Return the square of the minimum distance between ## cluster centers. ##---------------------------------------------------------------------- function d_sqr_min = min_sqr_dist_between_centers (V) k = rows (V); d_sqr_matrix = NaN(k, k); for i = 1 : (k - 1) Vi = V(i, :); for j = (i + 1) : k Vi_to_Vj = V(j, :) - Vi; d_sqr_matrix(i, j) = sum (Vi_to_Vj .* Vi_to_Vj); endfor endfor d_sqr_min = min (min (d_sqr_matrix)); endfunction ## Test input validation %!error %! xie_beni_index() %!error %! xie_beni_index(1) %!error %! xie_beni_index(1, 2) %!error %! xie_beni_index(1, 2, 3, 4) %!error %! xie_beni_index(1j, 2, 3) %!error %! xie_beni_index(1, [2 2], 3) %!error %! xie_beni_index([1 1], [2 2], 3j) fuzzy-logic-toolkit-0.6.1/inst/zmf.m000066400000000000000000000132231466512601400174200ustar00rootroot00000000000000## Copyright (C) 2011-2024 L. Markowsky ## ## This file is part of the fuzzy-logic-toolkit. ## ## The fuzzy-logic-toolkit is free software; you can redistribute it ## and/or modify it under the terms of the GNU General Public License ## as published by the Free Software Foundation; either version 3 of ## the License, or (at your option) any later version. ## ## The fuzzy-logic-toolkit is distributed in the hope that it will be ## useful, but WITHOUT ANY WARRANTY; without even the implied warranty ## of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with the fuzzy-logic-toolkit; see the file COPYING. If not, ## see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} zmf (@var{x}, @var{params}) ## @deftypefnx {Function File} {@var{y} =} zmf (@var{[x1 x2 ... xn]}, @var{[a b]}) ## ## For a given domain @var{x} and parameters @var{params} (or @var{[a b]}), ## return the corresponding @var{y} values for the Z-shaped membership function. ## ## The argument @var{x} must be a real number or a non-empty vector of strictly ## increasing real numbers, and @var{a} and @var{b} must be real numbers, with ## @var{a} < @var{b}. This membership function satisfies: ## ## @verbatim ## 1 if x <= a ## f(x) = 1 - 2 * ((x - a)/(b - a))^2 if a < x <= (a + b)/2 ## 2 * ((x - b)/(b - a))^2 if (a + b)/2 < x < b ## 0 if x >= b ## @end verbatim ## ## which always returns values in the range [0, 1]. ## ## The parameters a and b specify: ## ## @verbatim ## a == the rightmost point at which f(x) = 1 ## b == the leftmost point at which f(x) = 0 ## @end verbatim ## ## At the midpoint of the segment [a, b], the function value is 0.5: ## ## @verbatim ## f((a + b)/2) = 0.5 ## @end verbatim ## ## To run the demonstration code, type "@t{demo zmf}" (without the quotation ## marks) at the Octave prompt. ## ## @seealso{dsigmf, gauss2mf, gaussmf, gbellmf, pimf, psigmf, sigmf, smf, trapmf, trimf, zmf_demo} ## @end deftypefn ## Author: L. Markowsky ## Keywords: fuzzy-logic-toolkit fuzzy membership z-shaped ## Directory: fuzzy-logic-toolkit/inst/ ## Filename: zmf.m ## Last-Modified: 13 Jun 2024 function y = zmf (x, params) ## If the caller did not supply 2 argument values with the correct ## types, print an error message and halt. if (nargin != 2) error ("zmf requires 2 arguments\n"); elseif (!is_domain (x)) error ("zmf's first argument must be a valid domain\n"); elseif (!are_mf_params ('zmf', params)) error ("zmf's second argument must be a parameter vector\n"); endif ## Calculate and return the y values of the membership function on the ## domain x. a = params(1); b = params(2); a_b_ave = (a + b) / 2; b_minus_a = b - a; y_val = @(x_val) zmf_val (x_val, a, b, a_b_ave, b_minus_a); y = arrayfun (y_val, x); endfunction ##---------------------------------------------------------------------- ## Usage: y_val = zmf_val (x_val, a, b, a_b_ave, b_minus_a) ## ## zmf_val returns one value of the Z-shaped membership function, which ## satisfies: ## 1 if x <= a ## f(x) = 1 - 2 * ((x - a)/(b - a))^2 if a < x <= (a + b)/2 ## 2 * ((x - b)/(b - a))^2 if (a + b)/2 < x < b ## 0 if x >= b ## ## zmf_val is a private function, called only by zmf. Because zmf_val ## is not intended for general use -- and because the parameters a and b ## are checked for errors in the function zmf (defined above), the ## parameters are not checked for errors again here. ##---------------------------------------------------------------------- function y_val = zmf_val (x_val, a, b, a_b_ave, b_minus_a) ## Calculate and return a single y value of the Z-shaped membership ## function for the given x value and parameters specified by the ## arguments. if (x_val <= a) y_val = 1; elseif (x_val <= a_b_ave) y_val = 1 - 2 * ((x_val - a) / b_minus_a)^2; elseif (x_val < b) y_val = 2 * ((x_val - b) / b_minus_a)^2; else y_val = 0; endif endfunction %!demo %! x = 0:100; %! params = [40 60]; %! y1 = zmf(x, params); %! params = [25 75]; %! y2 = zmf(x, params); %! params = [10 90]; %! y3 = zmf(x, params); %! figure('NumberTitle', 'off', 'Name', 'zmf demo'); %! plot(x, y1, 'r;params = [40 60];', 'LineWidth', 2) %! hold on; %! plot(x, y2, 'b;params = [25 75];', 'LineWidth', 2) %! hold on; %! plot(x, y3, 'g;params = [10 90];', 'LineWidth', 2) %! ylim([-0.1 1.1]); %! xlabel('Crisp Input Value', 'FontWeight', 'bold'); %! ylabel('Degree of Membership', 'FontWeight', 'bold'); %! grid; %!test %! x = 0:10:100; %! params = [25 75]; %! y = [1 1 1 0.9800 0.8200 0.5000 0.1800 0.020000 0 0 0]; %! z = zmf(x, params); %! assert(z, y, 1e-4); ## Test input validation %!error zmf() %!error zmf(1) %!error zmf(1, 2, 3) %!error zmf([1 0], 2) %!error zmf(1, 2) %!error zmf(0:100, []) %!error zmf(0:100, [30]) %!error zmf(0:100, [90 80 30]) %!error zmf(0:100, 'abc') %!error zmf(0:100, '')