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## Copyright (C) 2011-2025 L. Markowsky <lmarkowsky@gmail.com>
##
## 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 <http://www.gnu.org/licenses/>.
## -*- 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
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