Characterization of Consistent Completion of Reciprocal Comparison Matrices

Algorithm 1

function [M, b, N]  = test(A,  P)

% A  is the matrix to be completed (if we do not know a_{ij}, then A(i,   j)=1

% P  is a  (0, 1)-matrix such that if we do not know a_{ij}, then  P(i,j)=1.

% if we know a_{ij}, then  P(i, j)=0.

% Use: [M, b, N]  = test(A,  P)

% M  = M_A; b  = b_A ;  N  = pseudo-inverse of the transpose of M_A

[n, m]=size(A);

n1  = (n∧2−n)/2;

n2 = sum(sum(P))/2;

n3 = n1−n2;

M  = zeros(n3, n);

k  = 1;

b  = zeros(n3, 1);

for i=1:n

    for j=i+1:n

    If  P(i,  j)==0

       M(k,  i)=1;  M(k,  j)=−1;

       b(k)=  log(A(i,  j));

       k=k+1;

    end

    end

end

M=M ′ ;

N=pinv(M ′ );

% Since there are numerical errors, a tolerance is used

if norm(M ′ *N*b−b) > 10∧(−10)

    disp(‘There is no consistent completion’)

else

    disp(‘There is consistent completion’)

end