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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_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
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