fuzzy.m

內涵模糊理論與類神經網路的程式碼...提供初學者做研究參考

% ==========================================================
% 
%           Neural Networks A Classroom Approach
%                     Satish Kumar
%             Copyright Tata McGraw Hill, 2004
%
%    MATLAB code that implements the fuzzification and 
%    defuzzification in fuzzy approximation example
%       Reference: Table 14.6 and 14.7;Pages 642-643
%
% ==========================================================

uodx = [-3 3];
uody = [-3 3];
uodz = [0 1];

xsets = [-3   -3   -2		% Left-center-right. 
         -2.5 -1.5 -0.5		% y-y-x or x-y-y means a half triangle	
         -1    0    1
          0.5  1.5  2.5
          2    3    3];

ysets = xsets; 				% symmetry used here

zsets = [0    0    0.25
         0.15 0.33 0.55
         0.45 0.66 0.85
         0.75 1    1]; 

% Find number of sets on each UOD
numxsets = size(xsets,1);
numysets = size(ysets,1);
numzsets = size(zsets,1);

for i = 1:numzsets
   areaz(i) = 0.5 * (zsets(i,3)-zsets(i,1)) * 1;
end

rulebase = [1 1 2 1 1
			   1 2 3 2 1
   			2 3 4 3 2
   			1 2 3 2 1
   			1 1 2 1 1];

[x,y] = meshgrid(-3:0.2:3,-3:0.2:3);
inx = x(1,:);
iny = inx;

for m = 1:size(x,1)
   inputx = inx(m);
   
   for n = 1:size(y,1)
      inputy = iny(n);
      
      for i = 1:numxsets
         if ((inputx - xsets(i,1))*(xsets(i,3) - inputx) >= 0)
            firex(i) = mem(inputx, xsets(i,:));
         else 
            firex(i) = 0;
         end
      end
      
      for i = 1:numysets
         if ((inputy - ysets(i,1))*(ysets(i,3) - inputy) >= 0)
            firey(i) = mem(inputy, ysets(i,:));
         else
            firey(i) = 0;
         end
      end
      
      for i = 1:numxsets
         for j = 1:numysets
            rulefire(i,j) = min(firex(i),firey(j));
         end
      end
      
      [k,l] = find(rulefire > 0);
      num = 0;
      den = 0;
      for i = 1:size(k)
         num = num + rulefire(k(i),l(i)) * zsets(rulebase(k(i),l(i)),2) * ...
            areaz(rulebase(k(i),l(i)));
         den = den + rulefire(k(i),l(i)) * areaz(rulebase(k(i),l(i)));
      end
      
      if den ~= 0
         func(m,n) = num/den;
      else
         func(m,n) = 0;
      end
      clear k l;
   end
end

figure(2)
subplot(2,2,2)
mesh(x,y,func)
xlabel('x');
ylabel('y');
zlabel('z');
title('(b)')
colormap(cool);

%generate the Gaussian
sigma = 1.5;

for i=1:31
    for j=1:31
        gauss(i,j) = exp(-((x(i,j))^2 + (y(i,j))^2)/(2*sigma^2));
    end
end
subplot(2,2,1)
mesh(x, y, gauss);
title('(a)')
xlabel('x');
ylabel('y');
zlabel('z');

subplot(2,2,3)
mesh(x,y,(gauss-func))
axis([-3 3 -3 3 -1 1])
title('(c)')
xlabel('x');
ylabel('y');
zlabel('Linear error');

subplot(2,2,4)
mesh(x,y,(gauss-func).^2)
title('(d)')
xlabel('x');
ylabel('y');
zlabel('Squared error');