% fzrelationdemo.m - fuzzy relation demonstration
% Define fuzzy relations much_older as:
%   mu(x,y)=0 if x <= y
%   mu(x,y)=(x-y)/20 if 0 <= x-y < 20
%   mu(x,y)=1 if x > y + 20
% Given Dana is (a) matured (b) exactly 43 years old
% infer Mary's age
% Both max-min and max-product relation composition rules are used.
% (C) 2005 by Yu Hen Hu
% created: 12/4/2005
% call fzcompose, fuzify, fzor

clear all, close all

% define fuzzy sets {children, teenager, young, 30something, middleage, matured, old}
% over age=[0:60];
age=[0:60];
M=fsgen(7,age); 
figure(1),plot(age,M');

[X,Y]=meshgrid(0:60,0:60);
Rmuch_older=(min(1,max(0,[X-Y]*0.05)))';  % R(x,y) is the relations x >> y
figure(2),imagesc(Rmuch_older),colormap('gray')

%%%%%%%% part (a) if dana is matured, what is mary's age

dana=[0 0 0 0 0 1 0]*M; % Dana's age is matured
mary=fzcompose(dana,Rmuch_older);

figure(3),plot(age,mary,'r',age,dana,'g')
legend('Mary', 'Dana'), title('(a) Fuzzy sets of ages of Mary and Dana')

mary1=fzcompose(dana,Rmuch_older,1); % max product composition
figure(4),plot(age,mary1,'r',age,dana,'g')
legend('Mary', 'Dana'), title('(a) Max-product solution')

%%%%%%%% part (b) if dana is matured, what is mary's age

danastar=43; % dana's age in years 
omega = fuzify(M,danastar,age); % 1 x size(M,1)
disp('compatibility omega = ');
disp(num2str(omega,4));

% gives compatibility (activation) of each fuzzy set.
danab=omega*M;
maryb=fzcompose(danab,Rmuch_older);
marystar=defuz(maryb,age);
disp(['If Dana is ' int2str(danastar) ', then Mary is ' int2str(marystar)]);

figure(5),
plot(age,maryb,'r',age,danab,'g'),hold on
stem([marystar danastar],[1 1]);
legend('Mary','Dana'), 
title([' (b) Dana is ' int2str(danastar) ', Mary is ' int2str(marystar)]);

maryb1=fzcompose(danab,Rmuch_older,1); % max product composition
marystar1=defuz(maryb1,age);
disp(['Use Max-product composition, Mary is ' int2str(marystar1)]);

figure(6),
plot(age,maryb1,'r',age,danab,'g'),hold on
stem([marystar1 danastar],[1 1]);
legend('Mary','Dana'), 
title([' (b) Max-product composition, Mary is ' int2str(marystar1)]);