approaching_fuzzy_2v.m

使用模糊系统方法来实现二维函数的逼近

%Fuzzy approaching 2
clear all;
close all;

T=0.1;
x1=-1:T:1;
x2=-1:T:1;

L=2;
h=0.2;
N=L/h+1;

for i=1:1:N%N MF
    for j=1:1:N
        e1(i)=-1+L/(N-1)*(i-1);
        e2(j)=-1+L/(N-1)*(j-1);
        gx(i,j)=0.52+0.1*e1(i)^3+0.28*e2(j)^3-0.06*e1(i)*e2(j);
    end
end

df=zeros(L/T+1,L/T+1);
cf=zeros(L/T+1,L/T+1);
for m=1:1:N%u1 change form 1 to N
    if m==1
        u1=trimf(x1,[-1,-1,-1+L/(N-1)]);%The first u1
    elseif m==N
        u1=trimf(x1,[1-L/(N-1),1,1]);%The last u1
    else
        u1=trimf(x1,[e1(m-1),e1(m),e1(m+1)]);
    end
    figure(1);
    hold on;
    plot(x1,u1);
    xlabel('x1');ylabel('Membership function');
    
    for n=1:1:N%u2 change form 1 to N
        if n==1
            u2=trimf(x2,[-1,-1,-1+L/(N-1)]);%The first u2
        elseif n==N
            u2=trimf(x2,[1-L/(N-1),1,1]);%The last u2
        else
            u2=trimf(x2,[e2(n-1),e2(n),e2(n+1)]);
        end
        figure(2);
        hold on;
        plot(x2,u2);
        xlabel('x2');ylabel('Membership function');
        
        for i=1:1:L/T+1
            for j=1:1:L/T+1
                d=df(i,j)+u1(i)*u2(j);
                df(i,j)=d;
                c=cf(i,j)+gx(m,n)*u1(i)*u2(j);
                cf(i,j)=c;
            end
        end
    end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
for i=1:1:L/T+1
    for j=1:1:L/T+1
        f(i,j)=cf(i,j)/df(i,j);
        y(i,j)=0.52+0.1*x1(i)^3+0.28*x2(j)^3-0.06*x1(i)*x2(j);
    end
end
figure(3);
subplot(211);
surf(x1,x2,f);
title('f(x)');
subplot(212);
surf(x1,x2,y);
title('g(x)');
figure(4);
surf(x1,x2,f-y);
title('Approaching error');