ProductInferenceEngine_1.m

x = [-5:.1:5];
y = x;

% X input MF's
xsmall = 1./(1+exp(-(-3)*(x-0)));
xlarge = 1./(1+exp(-(3)*(x-0)));

subplot(3,1,1);
hold on
plot(x,xsmall);
plot(x,xlarge);
xlabel('Universe X');
ylabel('MF Grade');
title('Input X Membership Functions');
legend('Small', 'Large')

% Y input MF's
ysmall = 1./(1+exp(-(-0.9)*(y-0)));
ylarge = 1./(1+exp(-(0.9)*(y-0)));

subplot(3,1,2);
hold on
plot(y,ysmall);
plot(y,ylarge);
xlabel('Universe Y');
ylabel('MF Grade');
title('Input Y Membership Functions');
legend('Small', 'Large')

% Z output MF's
zneglarge = 1./(1+exp(-(-4)*(x-(-3.5))));
znegsmall = exp(-0.5*(((x-(-1.7))/1.5).^2));
zpossmall = exp(-0.5*(((x-(1.7))/1.5).^2));
zposlarge = 1./(1+exp(-(4)*(x-(3.5))));

subplot(3,1,3);
hold on
plot(x,zneglarge);
plot(x,znegsmall);
plot(x,zpossmall);
plot(x,zposlarge);
xlabel('Universe Z');
ylabel('MF Grade');
title('Output Z Membership Functions');
legend('NegLarge', 'NegSmall', 'PosSmall', 'PosLarge')

%% Product Inference Engine (PIE)

% Crisp inputs are used as fuzzy singleton facts
xfacts = [-5 0 1];
yfacts = [-1 0 5];

% Evaluate X and Y membership functions at these fact values
% this output known as "firing strength" ?
xfacts_xsmall_MFgrade = 1./(1+exp(-(-3)*(xfacts-0)));
xfacts_xlarge_MFgrade = 1./(1+exp(-(3)*(xfacts-0)));
yfacts_ysmall_MFgrade = 1./(1+exp(-(-0.9)*(yfacts-0)));
yfacts_ylarge_MFgrade = 1./(1+exp(-(0.9)*(yfacts-0)));
  
% Rule 1, if x is small and y is small then z is neglarge
wR1 = xfacts_xsmall_MFgrade .* yfacts_ysmall_MFgrade;    % this is the "rule weight" from all inputs (antecedents)?
R1_zneglarge = wR1' * zneglarge;
% Rule 2, if x is small and y is large then z is negsmall
wR2 = xfacts_xsmall_MFgrade .* yfacts_ylarge_MFgrade;
R2_znegsmall = wR2' * znegsmall;
% Rule 3, if x is large and y is small then z is possmall
wR3 = xfacts_xlarge_MFgrade .* yfacts_ysmall_MFgrade;
R3_zpossmall = wR3' * zpossmall;
% Rule 4, if x is large and y is large then z is poslarge
wR4 = xfacts_xlarge_MFgrade .* yfacts_ylarge_MFgrade;
R4_zposlarge = wR4' * zposlarge;


%% Plot everything

for i=1:length(xfacts),
    % Plot Rule 1
    figure();
    subplot(4,3,1);
    hold on
    plot(x,xsmall);
    stem(xfacts(i),xfacts_xsmall_MFgrade(i)); % Small MF grade for x 
    xlabel('Universe X');
    ylabel('MF Grade');
    title('if x is small');
    legend('Small', sprintf('x = %i', xfacts(i)))

    subplot(4,3,2);
    hold on
    plot(y,ysmall);
    stem(yfacts(i),yfacts_ysmall_MFgrade(i)); % Small MF grade for y 
    xlabel('Universe Y');
    ylabel('MF Grade');
    title('and y is small');
    legend('Small', sprintf('y = %i', yfacts(i)))

    subplot(4,3,3);
    hold on
    plot(x,zneglarge);
    area(x,R1_zneglarge(i,:));
    temp = ones(length(x)) * wR1(i);
    plot(x,temp, '--');    % Product of x and y MF grades = rule weight? 
    xlabel('Universe Z');
    ylabel('MF Grade');
    title('then z is neg-large');
    legend('NegLarge MF', 'R1 NegLarge Output', 'R1 weight')

    % Plot Rule 2
    subplot(4,3,4);
    hold on
    plot(x,xsmall);
    stem(xfacts(i),xfacts_xsmall_MFgrade(i)); % Small MF grade for x 
    xlabel('Universe X');
    ylabel('MF Grade');
    title('if x is small');
    legend('Small', sprintf('x = %i', xfacts(i)))

    subplot(4,3,5);
    hold on
    plot(y,ylarge);
    stem(yfacts(i),yfacts_ylarge_MFgrade(i)); % Small MF grade for y 
    xlabel('Universe Y');
    ylabel('MF Grade');
    title('and y is large');
    legend('Large', sprintf('y = %i', yfacts(i)))

    subplot(4,3,6);
    hold on
    plot(x,znegsmall);
    area(x,R2_znegsmall(i,:));
    temp = ones(length(x)) * wR2(i);
    plot(x,temp, '--');    % Product of x and y MF grades = rule weight? 
    xlabel('Universe Z');
    ylabel('MF Grade');
    title('then z is neg-small');
    legend('NegLarge MF', 'R2 NegLarge Output', 'R2 weight')

    % Plot Rule 3
    subplot(4,3,7);
    hold on
    plot(x,xlarge);
    stem(xfacts(i),xfacts_xlarge_MFgrade(i)); % Large MF grade for x 
    xlabel('Universe X');
    ylabel('MF Grade');
    title('if x is large');
    legend('Large', sprintf('x = %i', xfacts(i)))

    subplot(4,3,8);
    hold on
    plot(y,ysmall);
    stem(yfacts(i),yfacts_ysmall_MFgrade(i)); % Small MF grade for y 
    xlabel('Universe Y');
    ylabel('MF Grade');
    title('and y is small');
    legend('Small', sprintf('y = %i', yfacts(i)))

    subplot(4,3,9);
    hold on
    plot(x,zpossmall);
    area(x,R3_zpossmall(i,:));
    temp = ones(length(x)) * wR3(i);
    plot(x,temp, '--');    % Product of x and y MF grades = rule weight? 
    xlabel('Universe Z');
    ylabel('MF Grade');
    title('then z is pos-small');
    legend('pos-small MF', 'R3 pos-small output', 'R3 weight')

    % Plot Rule 4
    subplot(4,3,10);
    hold on
    plot(x,xlarge);
    stem(xfacts(i),xfacts_xlarge_MFgrade(i)); % Large MF grade for x 
    xlabel('Universe X');
    ylabel('MF Grade');
    title('if x is large');
    legend('Large', sprintf('x = %i', xfacts(i)))

    subplot(4,3,11);
    hold on
    plot(y,ylarge);
    stem(yfacts(i),yfacts_ylarge_MFgrade(i)); % Large MF grade for y 
    xlabel('Universe Y');
    ylabel('MF Grade');
    title('and y is large');
    legend('Large', sprintf('y = %i', yfacts(i)))

    subplot(4,3,12);
    hold on
    plot(x,zposlarge);
    area(x,R4_zposlarge(i,:));
    temp = ones(length(x)) * wR4(i);
    plot(x,temp, '--');    % Product of x and y MF grades = rule weight? 
    xlabel('Universe Z');
    ylabel('MF Grade');
    title('then z is pos-large');
    legend('pos-large MF', 'R4 pos-large output', 'R4 weight')
end

%% CA Defuzzification

% determine center points for fuzzy outputs Z
% sigmoids are arbitrary, based on class slides
zneglarge_center = -4;  
zposlarge = 4;          
% gaussians, find 
znegsmall
zpossmall


% single point x,y example
figure()
hold on
area(x,R1_zneglarge(3,:));
temp = ones(length(x)) * wR1(3);
plot(x,temp, '--');
area(x,R2_znegsmall(3,:));
temp = ones(length(x)) * wR2(3);
plot(x,temp, '--');
area(x,R3_zpossmall(3,:));
temp = ones(length(x)) * wR3(3);
plot(x,temp, '--');
area(x,R4_zposlarge(3,:));
temp = ones(length(x)) * wR4(3);
plot(x,temp, '--');