VR13.m

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Citation:
% Enginoğlu, S., Memiş, S., 2018. A Configuration of Some Soft Decision-Making  
% Algorithms via fpfs-matrices. Cumhuriyet Science Journal, 39(4), 871-881 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Abbreviation of Journal Title: Cumhuriyet Sci. J.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% https://dergipark.org.tr/tr/download/article-file/605518
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% https://www.researchgate.net/profile/Serdar_Enginoglu2
% https://www.researchgate.net/profile/Samet_Memis2
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % Demo: 
% clc;
% clear all;
% % a and b are the fpfs-matrices
% % Product can be selected as 'AND' or 'OR'
% % s is a score matrix
% % dm is a decision matrix
% % op is a optimum alternatives' matrix 
% a=rand(5,3);
% b=rand(5,4);
% [s,dm,op]=VR13(a,b,'AND');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [s,dm,op]=VR13(a,b,Product)
if size(a,1)==size(b,1)
%% Step 1
[m,n1]=size(a);
[~,n2]=size(b);
%% Step 2
    for i=1:m
        for j=1:n1
            for k=1:n2
                p=n2*(j-1)+k;
                if Product=="AND"
                    c(i,p)=min(a(i,j),b(i,k));
                elseif Product=="OR"
                    c(i,p)=max(a(i,j),b(i,k));   
                end
            end
        end
    end
%% Step 3
    for i=1:m
        for j=1:n1
            for k=1:n2
                p=n2*(j-1)+k;
                d(i,p)=(a(i,j)+b(i,k))/2;
            end
        end
    end
%% Step 4   
    for i=1:m
        for p=1:n1*n2
            e(i,p)=min(c(i,p)+d(i,p));
        end
    end
%% Step 5
    for p=1:n1*n2
        f(1,p)=e(1,p);
    end
    for i=2:m
        for p=1:n1*n2
            if e(i,p)>=max(e(:,p))
                f(i,p)=1;
            else
                f(i,p)=0;
            end
        end
    end
%% Step 6
    for i=2:m
        s(i-1,1)=sum(f(1,:).*f(i,:));
    end
%% Step 7
dm(:,1)=normalise(s);
count=1;
    for i=1:m-1
         if(s(i)==max(s))
            op(count)=i;
            count=count+1;
         end
    end
else
    error('Row numbers of the matrices must be the same.');     
end
end

function na=normalise(a)
[m,n]=size(a);
    if m==1 || n==1
        if max(a)~=min(a)
            na=(a-min(a))/(max(a)-min(a));
        else
            na=ones(m,n);
        end
    end
end