区间二型模糊逻辑系统

%% train_nsfls2.m %% Tune the parameters of an interval type-2 non-singleton type-2 FLS %% when the antecedent membership functions are Gaussian primary %% membership functions with uncertain means and the input membership %% functions are Gaussian primary membership functions with uncertain %% standard deviations, using some input�output training data. %% M1,M2, sigma are mxn matrix denotes the mean and std of %% antecedent Gaussian MFs (N rules, with n antecedent in each rule); %% c1,c2 are Nx1 vectors, which denote the COS of consequents; %% sn1,sn2 are the input std; %% X is input matrix, Lxant matrix, each row is onw input. %% D is Lx1 vector which denotes the desired output %% alpha is the step size for tuning M, sigma, c1,c2; %% alpha4 is the step size for tuning sn; function [M1,M2,c1,c2,sigma,sn1,sn2]=train_nsfls_type2_2(X,D,M1,M2,sigma,c1,c2,sn1,sn2,alpha,alpha4); [L,ant]=size(X); [N,ant]=size(M); %%%%%% Following are the training for type-2 FLS %%%%%%% for i=1:L U=[]; MU1=[]; UU=[]; LL=[]; for j=1:N Uu=1; Ll=1; for m=1:ant if X(i,m) <= M1(j,m) xupp=((sn2(m)^2)*M1(j,m)+(sigma(j,m)^2)*X(i,m))/(sn2(m)^2+sigma(j,m)^2); xlow=((sn1(m)^2)*M2(j,m)+(sigma(j,m)^2)*X(i,m))/(sn1(m)^2+sigma(j,m)^2); elseif X(i,m)>M1(j,m) & X(i,m)<= (M1(j,m)+M2(j,m))/2-sn1(m)^2*(M2(j,m)-M1(j,m))/(2*sigma(j,m)^2) xupp=X(i,m); xlow=((sn1(m)^2)*M2(j,m)+(sigma(j,m)^2)*X(i,m))/(sn1(m)^2+sigma(j,m)^2); elseif X(i,m)>(M1(j,m)+M2(j,m))/2-sn1(m)^2*(M2(j,m)-M1(j,m))/(2*sigma(j,m)^2) &... X(i,m)<(M1(j,m)+M2(j,m))/2+sn1(m)^2*(M2(j,m)-M1(j,m))/(2*sigma(j,m)^2) xupp=X(i,m); xlow=(M1(j,m)+M2(j,m))/2; elseif X(i,m)>=(M1(j,m)+M2(j,m))/2+sn1(m)^2*(M2(j,m)-M1(j,m))/(2*sigma(j,m)^2) & X(i,m) < M2(j,m) xupp=X(i,m); xlow=((sn1(m)^2)*M1(j,m)+(sigma(j,m)^2)*X(i,m))/(sn1(m)^2+sigma(j,m)^2); elseif X(i,m) >= M2(j,m) xupp=((sn2(m)^2)*M2(j,m)+(sigma(j,m)^2)*X(i,m))/(sn2(m)^2+sigma(j,m)^2); xlow=((sn1(m)^2)*M1(j,m)+(sigma(j,m)^2)*X(i,m))/(sn1(m)^2+sigma(j,m)^2); end P=[sigma(j,m),M1(j,m),M2(j,m)]; [uu,ll]=gausstype2(xupp,P); uu=uu*gaussmf(xupp,[sn2(m), X(i,m)]); [tmp,ll]=gausstype2(xlow,P); ll=ll*gaussmf(xlow,[sn1(m), X(i,m)]); Uu=Uu*uu; Ll=Ll*ll; end UU=[UU,Uu]; LL=[LL,Ll]; end [r_out,I2l,I2u,wr]= rightpoint(c2',LL,UU); [l_out,I1u,I1l,wl]= leftpoint(c1',LL,UU); f=(l_out+r_out)/2; e=D(i)-f; fa1=wl/sum(wl); fa2=wr/sum(wr); %%% Select MFs contributed to the right-most ME10=M1; ME20=M2; sn20=sn2; sn10=sn1; LE=length(I2u); for t=1:LE for k=1:ant if X(i,k)<=M1(I2u(t),k) l=I2u(t); M1(l,k)=M1(l,k)+alpha*e*0.5*((X(i,k)-M1(l,k))/(sigma(l,k)^2+sn2(k)^2))... *(c2(l)-r_out)*wr(l)/sum(wr); sigma(l,k)=sigma(l,k)+alpha*e*0.5*(((sigma(l,k)*(X(i,k)-ME10(l,k))^2)/(sigma(l,k)^2+sn2(k)^2)^2)... *(c2(l)-r_out)*wr(l)/sum(wr)); sn20(k)=sn20(k)+alpha4*e*0.5*(((sn2(k)*(X(i,k)-ME10(l,k))^2)/(sigma(l,k)^2+sn2(k)^2)^2)... *(c2(l)-r_out)*wr(l)/sum(wr)); elseif X(i,k)>=M2(I2u(t),k) l=I2u(t); M2(l,k)=M2(l,k)+alpha*e*0.5*((X(i,k)-M2(l,k))/(sigma(l,k)^2+sn2(k)^2))... *(c2(l)-r_out)*wr(l)/sum(wr); sigma(l,k)=sigma(l,k)+alpha*e*0.5*(((sigma(l,k)*(X(i,k)-ME20(l,k))^2)/(sigma(l,k)^2+sn2(k)^2)^2)... *(c2(l)-r_out)*wr(l)/sum(wr)); sn20(k)=sn20(k)+alpha4*e*0.5*(((sn2(k)*(X(i,k)-ME20(l,k))^2)/(sigma(l,k)^2+sn2(k)^2)^2)... *(c2(l)-r_out)*wr(l)/sum(wr)); end end end LE=length(I2l); for t=1:LE for k=1:ant l=I2l(t); if X(i,k)<=(M1(l,k)+M2(l,k))/2-sn1(k)^2*(M2(l,k)-M1(l,k))/(2*sigma(l,k)^2) M2(l,k)=M2(l,k)+alpha*e*0.5*((X(i,k)-M2(l,k))/(sigma(l,k)^2+sn1(k)^2))... *(c2(l)-r_out)*wr(l)/sum(wr); sigma(l,k)=sigma(l,k)+alpha*e*0.5*(((sigma(l,k)*(X(i,k)-ME20(l,k))^2)/(sigma(l,k)^2+sn1(k)^2)^2)... *(c2(l)-r_out)*wr(l)/sum(wr)); sn10(k)=sn10(k)+alpha4*e*0.5*(((sn1(k)*(X(i,k)-ME20(l,k))^2)/(sigma(l,k)^2+sn1(k)^2)^2)... *(c2(l)-r_out)*wr(l)/sum(wr)); elseif X(i,k)>=(M1(l,k)+M2(l,k))/2+sn1(k)^2*(M2(l,k)-M1(l,k))/(2*sigma(l,k)^2) M1(l,k)=M1(l,k)+alpha*e*0.5*((X(i,k)-M1(l,k))/(sigma(l,k)^2+sn1(k)^2))... *(c2(l)-r_out)*wr(l)/sum(wr); sigma(l,k)=sigma(l,k)+alpha*e*0.5*(((sigma(l,k)*(X(i,k)-ME10(l,k))^2)/(sigma(l,k)^2+sn1(k)^2)^2)... *(c2(l)-r_out)*wr(l)/sum(wr)); sn10(k)=sn10(k)+alpha4*e*0.5*(((sn1(k)*(X(i,k)-ME10(l,k))^2)/(sigma(l,k)^2+sn1(k)^2)^2)... *(c2(l)-r_out)*wr(l)/sum(wr)); end end end %%% Select MFs contributed to the left-most LE=length(I1l); for t=1:LE for k=1:ant l=I1l(t); if X(i,k)<=(M1(l,k)+M2(l,k))/2-sn1(k)^2*(M2(l,k)-M1(l,k))/(2*sigma(l,k)^2) M2(l,k)=M2(l,k)+alpha*e*0.5*((X(i,k)-M2(l,k))/(sigma(l,k)^2+sn1(k)^2))... *(c1(l)-l_out)*wl(l)/sum(wl); sigma(l,k)=sigma(l,k)+alpha*e*0.5*(((sigma(l,k)*(X(i,k)-ME20(l,k))^2)/(sigma(l,k)^2+sn1(k)^2)^2)... *(c1(l)-l_out)*wl(l)/sum(wl)); sn10(k)=sn10(k)+alpha4*e*0.5*(((sn1(k)*(X(i,k)-ME20(l,k))^2)/(sigma(l,k)^2+sn1(k)^2)^2)... *(c1(l)-l_out)*wl(l)/sum(wl)); elseif X(i,k)>=(M1(l,k)+M2(l,k))/2+sn1(k)^2*(M2(l,k)-M1(l,k))/(2*sigma(l,k)^2) M1(l,k)=M1(l,k)+alpha*e*0.5*((X(i,k)-M1(l,k))/(sigma(l,k)^2+sn1(k)^2))... *(c1(l)-l_out)*wl(l)/sum(wl); sigma(l,k)=sigma(l,k)+alpha*e*0.5*(((sigma(l,k)*(X(i,k)-ME10(l,k))^2)/(sigma(l,k)^2+sn1(k)^2)^2)... *(c1(l)-l_out)*wl(l)/sum(wl)); sn10(k)=sn10(k)+alpha4*e*0.5*(((sn1(k)*(X(i,k)-ME10(l,k))^2)/(sigma(l,k)^2+sn1(k)^2)^2)... *(c1(l)-l_out)*wl(l)/sum(wl)); end end end LE=length(I1u); for t=1:LE for k=1:ant if X(i,k)<=M1(I1u(t),k) l=I1u(t); M1(l,k)=M1(l,k)+alpha*e*0.5*((X(i,k)-M1(l,k))/(sigma(l,k)^2+sn2(k)^2))... *(c1(l)-l_out)*wl(l)/sum(wl); sigma(l,k)=sigma(l,k)+alpha*e*0.5*(((sigma(l,k)*(X(i,k)-ME10(l,k))^2)/(sigma(l,k)^2+sn2(k)^2)^2)... *(c1(l)-l_out)*wl(l)/sum(wl)); sn20(k)=sn20(k)+alpha4*e*0.5*(((sn2(k)*(X(i,k)-ME10(l,k))^2)/(sigma(l,k)^2+sn2(k)^2)^2)... *(c1(l)-l_out)*wl(l)/sum(wl)); elseif X(i,k)>=M2(I1u(t),k) l=I1u(t); M2(l,k)=M2(l,k)+alpha*e*0.5*((X(i,k)-M2(l,k))/(sigma(l,k)^2+sn2(k)^2))... *(c1(l)-l_out)*wl(l)/sum(wl); sigma(l,k)=sigma(l,k)+alpha*e*0.5*(((sigma(l,k)*(X(i,k)-ME20(l,k))^2)/(sigma(l,k)^2+sn2(k)^2)^2)... *(c1(l)-l_out)*wl(l)/sum(wl)); sn20(k)=sn20(k)+alpha4*e*0.5*(((sn2(k)*(X(i,k)-ME20(l,k))^2)/(sigma(l,k)^2+sn2(k)^2)^2)... *(c1(l)-l_out)*wl(l)/sum(wl)); end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% sn2=sn20; sn1=sn10; fa1=wr'/sum(wr); fa2=wl'/sum(wl); c1=c1+alpha*e*fa1/2; c2=c2+alpha*e*fa2/2; %%%% After Training, The type-2 MFs should be reconstructed for l=1:N for k=1:ant if sigma(l,k) < 0 sigma(l,k)=abs(sigma(l,k)); end if sn2(k) > sigma(l,k) sn2(k)=sigma(l,k); end if sn1(k) < 0 sn1(k)=abs(sn1(k)); end if sn2(k) < 0 sn2(k)=abs(sn2(k)); end if sn2(k)<sn1(k) sn2(k)=sn1(k); sn1(k)=sn20(k); end if sn2(k) > sigma(l,k) sn2(k)=sigma(l,k); end end end mc2=max([c2,c1]'); mc1=min([c2,c1]'); c2=mc2'; c1=mc1'; ME1=[]; ME2=[]; for t=1:N P=[M2(t,:)',M1(t,:)']'; m2=max(P); m1=min(P); ME1=[ME1,m1']; ME2=[ME2,m2']; end M1=ME1'; M2=ME2'; end