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CA_defuzz.m

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+%_____________________________________________________________________%
+
+    %                 Authour       :      Ali Rezaei                %
+    %                 Email         :    rz.97.eng@gmail.com         %
+
+    %                   Center Average Defuzzifier                   %
+
+%_____________________________________________________________________%
+
+%  Custom defuzzification functions must be of the form
+%     y = customdefuzz(x,ymf), where x is the vector of 
+% values in the membership function input range and ymf 
+% contains the values of the membership function for each x value.
+
+
+% It is better if the output MFs are not overlapped.
+
+function out= CA_defuzz(x,ymf)
+    x=reshape(x,1,[]);
+    ymf=reshape(ymf,1,[]);
+    loc_x = islocalmax(ymf);
+    loc_x(1)=1;
+    loc_x(end)=1;
+    xx=x(loc_x);
+    w=ymf(loc_x);
+    out=(w*(xx'))/sum(w,"all");
+end
+
+% ____________________ End of the program. _______________________ % 

example.m

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+%_____________________________________________________________________%
+
+    %                 Authour       :      Ali Rezaei                %
+    %                 Email         :    rz.97.eng@gmail.com         %
+
+%                 Sample code for Center Average Defuzzifier         %
+%                  A Course in Fuzzy Systems and Control
+%                        Book by Li-Xin Wang
+%                           Problem 10 . 2 
+
+%_____________________________________________________________________%
+%% init
+clc; close all; clear;
+
+%% Data Set
+h=0.04;
+xx=-1:h:1;
+N=numel(xx);
+yy=sin(xx.*pi)+cos(xx.*pi)+sin(xx.*pi).*cos(xx.*pi);
+yy_sort=sort(yy);
+x_sort=[];
+yy_sort=unique(yy_sort);
+yy_sort=[yy_sort(1:13) yy_sort(15:end)];
+Ny=numel(yy_sort);
+for i=1:Ny
+    j=find(yy==yy_sort(i));
+    x_sort=[x_sort j(end)];
+end
+dd=1*(yy_sort(2:end)-yy_sort(1:end-1));
+dd=max(dd)/2;
+
+%% Defining the Fuzzy Interface System
+fis_10_2=mamfis;
+fis_10_2=addInput(fis_10_2,[min(xx) max(xx)],"Name","x");
+fis_10_2=addOutput(fis_10_2,[min(yy) max(yy)],"Name","y");
+fis_10_2.AndMethod='prod';
+fis_10_2.OrMethod='probor';
+fis_10_2.ImplicationMethod='prod';
+fis_10_2.AggregationMethod='sum';
+fis_10_2.DefuzzificationMethod='CA_defuzz'; 
+
+%% Input membership functions
+fis_10_2=addMF(fis_10_2,'x','trimf',[xx(1),xx(1),xx(1)+h]);
+for i=1:N-2
+    fis_10_2=addMF(fis_10_2,'x','trimf',[xx(i:i+2)]);
+end
+fis_10_2=addMF(fis_10_2,'x','trimf',[xx(end-1),xx(end),xx(end)+0.1*h]);
+
+%% Output membership functions
+for i=1:Ny
+    fis_10_2=addMF(fis_10_2,'y','trimf',[yy_sort(i)-dd yy_sort(i) yy_sort(i)+dd ]);
+end
+
+
+%% Defining Rules
+%Each row of the array contains one rule in the following format.
+    % Column 1 - Index of membership function for input
+    % Column 2 - Index of membership function for output
+    % Column 3 - Rule weight (from 0 to 1)
+    % Column 4 - Fuzzy operator (1 for AND, 2 for OR)
+fis_10_2.Rules=[]; % reset Rules
+for i=1:Ny
+    rule=[x_sort(i) i 1 1];
+    fis_10_2 = addRule(fis_10_2,rule);
+end
+% Due to the sorting output values and removing repeated parameters these
+% two rules should added to the rules; 
+rule=[1 1 1 1];
+fis_10_2 = addRule(fis_10_2,rule);
+rule=[5 13 1 1];
+fis_10_2 = addRule(fis_10_2,rule);
+%% Approximation 
+N_p_fis=15000; % number of plot points
+x_app=-1:h:1;
+y_exact=sin(x_app.*pi)+cos(x_app.*pi)+sin(x_app.*pi).*cos(x_app.*pi);
+y_app=zeros(1,numel(x_app));
+opt_eval=evalfisOptions('NumSamplePoints',N_p_fis);
+for i=1:numel(x_app)
+    y_app(i)=evalfis(fis_10_2,x_app(i),opt_eval); 
+end
+error=y_app-y_exact;
+e_max=max(abs(error));
+
+%% Plotting results 
+figure()
+    plotmf(fis_10_2,"input",1,N_p_fis/15)
+figure()
+    plotmf(fis_10_2,"output",1,5*N_p_fis)
+figure()
+    plot(x_app,y_exact,'--','LineWidth',3)
+    hold on
+    plot(x_app,y_app,'LineWidth',2.5)
+    legend('Actual function','Approximation')
+    grid
+figure()
+    plot(x_app,y_app,'LineWidth',1.5)
+    hold on
+    plot(xx,yy,'rX','MarkerSize',9)
+    grid
+    legend('Approximation','Data Base')
+
+