Efficient weight vectors from pairwise comparison matrices

Sándor Bozóki, János Fülöp

Published 2016-02-10Version 1

Pairwise comparison matrices are frequently applied in multi-criteria decision making. A weight vector is called efficient if no other weight vector is at least as good in approximating the elements of the pairwise comparison matrix, and strictly better in at least one position. Linear programs are proposed to test whether a given weight vector is efficient. A finite algorithm is presented to improve an inefficient weight vector, as well as to find an efficient dominating weight vector. Both the principal right eigenvector and the average of weight vectors calculated from the spanning trees can be inefficient as numerical examples show.