%	Compositional rule of inference%	Copyright by Jyh-Shing Roger Jang, 6-2-93.%	(Tested on Matlab version 4.0a, HP workstation)n = 31; m = 31;x = linspace(0, 10, n)';y = linspace(0, 40, m)';coef = [-0.5; 8; 0];y_val = polyval(coef, x);subplot(221);plot(x,y_val);xlabel('X'); ylabel('Y'); title('A Crisp Relation');z1 = zeros(m, n); z2 = zeros(m, n);for i=1:n,	a = 4; b = 3; c = y_val(i);	z1(:, i) = gbell_mf(y, [a, b, c]);endfor i=1:n,	a = 1; b = 3; c = 5;	z2(i,:) = gbell_mf(x', [a, b, c]);endsubplot(222);pcolor(x, y, z1);shading interp;colormap(gray);xlabel('X'); ylabel('Y'); title('A Fuzzy Relation');figure;subplot(221);mesh(x, y, z1)set(gca, 'box', 'on');view(-20, 60);xlabel('X'); ylabel('Y'); zlabel('Membership Grades');title('(a) Fuzzy Relation F on X and Y');subplot(222);mesh(x, y, z2)set(gca, 'box', 'on');view(-20, 60);xlabel('X'); ylabel('Y'); zlabel('Membership Grades');title('(b) Cylindrical Extension of A');colormap('default');intersection = min(z1, z2);subplot(223);mesh(x, y, min(z1, z2))set(gca, 'box', 'on');view(-20, 60);xlabel('X'); ylabel('Y'); zlabel('Membership Grades');title('(c) Minimum of (a) and (b)');projection = intersection;for i = 1:m,	maximum = -10e6;	for j=n:-1:1,		if (projection(i,j) > maximum)			maximum = projection(i,j);		else			projection(i,j) = maximum;		end	endend		subplot(224);mesh(x, y, projection)set(gca, 'box', 'on');view(-20, 60);xlabel('X'); ylabel('Y'); zlabel('Membership Grades');title('(d) Projection of (c) onto Y');