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Author: luukka76

Mainfile.m

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+% Mainfiles purpose is to show how to use n-ary TOPSIS method
+% that uses n-ary norm operators to set preference for either positive
+% ideal solution or negative ideal solution depending on the practical
+% problem. It was published in
+
+% P. Luukka, N—ary norm operators and TOPSIS, 2020 IEEE International 
+% Conference on Fuzzy Systems (FUZZ-IEEE), Glasgow, UK, 2020, pp. 1-6, 
+% doi: 10.1109/FUZZ48607.2020.9177580.
+
+
+%First lets create artificial data of ten alternatives and five criteria:
+c=10;
+data=c*randn(10,5);
+%Define parameters p for Minkowski metric (1=Manhattan distance,2=Euclidean distance etc)
+%and parameter values for fuzzy union (w) and intersection (w2) operators
+p=1;  w=2; w2=5;
+%See more information about these from the proceedings.
+
+%Define whether criteria is benefit criteria or cost criteria in crit
+%vector 1=benefit, 2=cost.
+crit=[1 1 1 2 1]; %in this example fourth would be cost criteria and others benefit
+
+[cc,PISB,NISB]=narytopsis(data,p,w,w2,crit)
+
+%For output of the function you get:
+%cc = closeness coefficient values for ten alternatives
+%PISB = distance to positive ideal solution
+%NISB = distance to negative ideal solution 
+
+%You can get the ordering of the alternatives by sorting CC to descending order
+[Y,I]=sort(cc,'descend');
+
+%Order of the attributes:
+Order=I'

distM.m

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+function d=distM(x,y,p)
+[m,n]=size(x);
+d=1/n*(sum(abs(x-y ).^p).^(1/p));

i_yager.m

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+function mu=i_bd(a,b,w)
+mu=1-min([1,((1-a)^w+(1-b)^w)^(1/w)]);

narytopsis.m

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+function [c,Dplus,Dminus]=topsis(data,p,w,w2,crit)
+x=data;
+[m,n]=size(x);
+a=zeros(m,n);
+%Normalization to unit interval:
+a=normalization(x);
+
+%Positive and negative ideal solutions:
+PIS=zeros(1,n);
+NIS=zeros(1,n);
+for j=1:n
+     if crit(j)==1   
+        PIS(j)=recursivetconorm(a(:,j)',w);
+        NIS(j)=recursivetnorm(a(:,j),w2);
+     else
+        NIS(j)=recursivetconorm(a(:,j)',w);
+        PIS(j)=recursivetnorm(a(:,j),w2);    
+     end
+end
+
+%Distances to PIS and NIS
+ DPISB=zeros(1,m);
+ DNISB=zeros(1,m);
+for i=1:m
+   Dplus(i)=distM(PIS,a(i,:),p); 
+   Dminus(i)=distM(NIS,a(i,:),p); 
+end
+%Closeness coefficient: 
+ c=zeros(1,m);
+ for i=1:m
+     c(i)=Dminus(i)/(Dplus(i)+Dminus(i));
+ end

normalization.m

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+function data_v=normalization2(data)
+%scaling data between [0,1]
+[m,n]=size(data);
+data_v=data;
+mins_v = min(data_v);
+Ones = ones(size(data_v));
+data_v = data_v+Ones*diag(abs(mins_v));
+maxs_v = max(data_v);
+data_v = data_v*diag(maxs_v.^(-1));

recursivetconorm.m

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+function unorm=tconormstandardn(A,w)
+[n,m]=size(A);
+unorm=u_yager(A(1),A(2),w);
+for i=2:n
+    unorm=u_yager(A(i),unorm,w);
+end

recursivetnorm.m

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+function inorm=tnormstandardn(A,w)
+[n,m]=size(A);
+inorm=i_yager(A(1),A(2),w);
+for i=2:n
+    inorm=i_yager(A(i),inorm,w);
+end

topsisdistpnary.m

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+function [c,Dplus,Dminus,PIS,NIS,a]=topsis(data,p,w)
+x=data;
+[m,n]=size(x);
+a=zeros(m,n);
+%Normalization:
+a=normalization2(x);
+
+%Positive and negative ideal solutions:
+PIS=zeros(1,n);
+NIS=zeros(1,n);
+w2=2;
+for j=1:n
+%    PIS(j)=max(a(:,j));
+%    NIS(j)=min(a(:,j));
+%    PIS(j)=tconormstandardn(a(:,j));
+%    PIS(j)=tconormprob(a(:,j)');
+%    PIS(j)=tconormluka(a(:,j)');
+%    PIS(j)=tconormdrastic(a(:,j)');
+    PIS(j)=recursivetconorm(a(:,j)',w);
+
+    NIS(j)=recursivetnorm(a(:,j),w2);
+%    NIS(j)=tnormstandardn(a(:,j));
+%    NIS(j)=tnormprob(a(:,j)');
+%    NIS(j)=tnormluka(a(:,j)');
+end
+
+%Distances to PIS and NIS
+ DPISB=zeros(1,m);
+ DNISB=zeros(1,m);
+% m1=1;
+% q=1;
+%p=2;
+for i=1:m
+   Dplus(i)=distM(PIS,a(i,:),p); 
+   Dminus(i)=distM(NIS,a(i,:),p); 
+end
+%Closeness coefficient: 
+ c=zeros(1,m);
+ for i=1:m
+%     c(i)=DNIS(i)/(DPIS(i)+DNIS(i));
+     c(i)=Dminus(i)/(Dplus(i)+Dminus(i));
+ end

u_yager.m

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+function mu=u_Yager(a,b,w)
+
+mu=min([1,(a^w+b^w)^(1/w)]);