General Type-2 FLSs.zip_Type-2_Type-2 Fuzzy_type 2 fuzzy_二型模糊_二型

%% weighted_avg.m %% Function to extend the weighed average of crisp numbers to %% the case where all the quantities involved are type-1 sets. %% It implements the generalized centroid in Equation (9-11) in %% the book Uncertain Rule-Based Fuzzy Logic Systems: Introduction %% and New Directions, by Jerry M. Mendel, and published by %% Prentice-Hall, 2000. %% Written by Nilesh N. Karnik - July 22,1998 %% For use with MATLAB 5.1 or higher. %% NOTE : This program uses an algorithm similar to %% "extend_nary2.m"; therefore, it is slow, but uses less memory %% than "extend_nary1.m". %% Outputs : "out" and "mem" (column vectors) are, respectively, %% the domain and the memberships of the result of the extended %% weighted average operation. %% Inputs : "Zout" and "Zmem" are "M x Nz" matrices, containing the %% domain elements and memberships of the "M" type-1 sets "Z_i"s - see %% Eq. (9-11). "Wout" and "Wmem" are "M x Nw" matrices, containing %% the domain elements and memberships of the "M" type-1 "W_i"s - see %% Eq. (9-11). The domain of each "Z_i" is assumed to contain "Nz" %% elements and that of each "W_i" is assumed to contain "Nw" elements. %% If "tnorm" (scalar) is < 0, minimum t-norm is used, otherwise %% product t-norm is used. Here, "step" (scalar) is a required %% parameter. In order to save memory, the domain of the output type-1 %% set is taken to be "[minz : step : maxz]", where %% "minz = min(min(Zout))" and "maxz = max(max(Zout))". Note that %% since this is a weighted average of the "Z_i"s, the smallest possible %% domain point in the output set is "minz" and the largest possible is %% "maxz". %% Note 1 : The t-conorm used is maximum. %% Note 2 : The notation in this program is somewhat different than %% that in "extend_nary1.m" and "extend_nary2.m", but it conforms with %% the notation in Eq. (9-11) . %% Note 3 : Since type-reduction calculations can be represented as %% extended weighted average calculations, this program can be used %% for type-reduction calculations in Chapter 9. function[out,mem] = weighted_avg(Zout,Zmem,Wout,Wmem,tnorm,step) [M,Nz] = size(Zout) ; Nw = size(Wout,2) ; Zout1 = Zout ; Zmem1 = Zmem ; Wout1 = Wout ; Wmem1 = Wmem ; if tnorm < 0, tnorm_op = 'min' ; else tnorm_op = 'prod' ; end %%% if tnorm %% Points for the output minz = min(min(Zout)) ; maxz = max(max(Zout)) ; out = [minz : step : maxz] ; mem = zeros(size(out)) ; count_Z = Nz^(M-1) ; count_W = Nw^(M-1) ; temp1 = zeros(1,Nz) ; temp2 = temp1 ; temp3 = zeros(1,Nw) ; temp4 = temp3 ; temp5 = temp3 ; for i6 = 1 : count_Z, for i4 = 1 : Nz, Zpoint = Zout1(:,i4)*ones(1,Nw) ; memZ = feval(tnorm_op,Zmem1(:,i4)) ; num_mat = Zpoint .* Wout1 ; for i1 = 1 : count_W, answer = sum(num_mat)./sum(Wout1) ; ind = round((answer - out(1))/step) + 1 ; memW = feval(tnorm_op,Wmem1) ; if tnorm < 0,, memout = min(memW,memZ) ; else memout = memZ.*memW ; end %% if minflag for i3 = 1 : Nw, mem(ind(i3)) = max(mem(ind(i3)) , memout(i3)) ; % max t-conorm end %% if i3 temp5(1:Nw-1) = num_mat(M,2:Nw) ; temp5(Nw) = num_mat(M,1) ; num_mat(M,:) = temp5 ; temp3(1:Nw-1) = Wout1(M,2:Nw) ; temp3(Nw) = Wout1(M,1) ; Wout1(M,:) = temp3 ; temp4(1:Nw-1) = Wmem1(M,2:Nw) ; temp4(Nw) = Wmem1(M,1) ; Wmem1(M,:) = temp4 ; for i2 = 1 : M-1, if mod(i1,Nw^i2) == 0, temp5(1:Nw-1) = num_mat(M-i2,2:Nw) ; temp5(Nw) = num_mat(M-i2,1) ; num_mat(M-i2,:) = temp5 ; temp3(1:Nw-1) = Wout1(M-i2,2:Nw) ; temp3(Nw) = Wout1(M-i2,1) ; Wout1(M-i2,:) = temp3 ; temp4(1:Nw-1) = Wmem1(M-i2,2:Nw) ; temp4(Nw) = Wmem1(M-i2,1) ; Wmem1(M-i2,:) = temp4 ; end %% if mod(i1,Nw^i2) end %%% for i2 end %%% for i1 end %% for i4 temp1(1:Nz-1) = Zout1(M,2:Nz) ; temp1(Nz) = Zout1(M,1) ; Zout1(M,:) = temp1 ; temp2(1:Nz-1) = Zmem1(M,2:Nz) ; temp2(Nz) = Zmem1(M,1) ; Zmem1(M,:) = temp2 ; for i5 = 1 : M-1, if mod(i6,Nz^i5) == 0, temp1(1:Nz-1) = Zout1(M-i5,2:Nz) ; temp1(Nz) = Zout1(M-i5,1) ; Zout1(M-i5,:) = temp1 ; temp2(1:Nz-1) = Zmem1(M-i5,2:Nz) ; temp2(Nz) = Zmem1(M-i5,1) ; Zmem1(M-i5,:) = temp2 ; end %% if mod(i1,N^i5) end %%% for i5 end %%% for i6 return ;