An empirical analysis of the use of the Analytic Hierarchy Process for estimating membership values in a fuzzy set

Abstract

The Analytic Hierarchy Process (AHP) is now a popular multicriteria decision-making method, and has been applied in many diverse areas despite the debate on its theoretical foundations. Many researchers have been using the pairwise comparison matrix and the eigenvector method suggested by Saaty for obtaining priority ratings of the decision alternatives in an AHP hierarchy. These priority ratings have been used as estimates of fuzzy membership values of the elements (called ‘alternatives’ in AHP) of a fuzzy set. Triantaphyllou and Mann have argued that Saaty's scale and the eigenvector method are inadequate for estimating fuzzy membership values. This paper points out the limitations in the arguments of Triantaphyllou and Mann about the eigenvector method. It primarily concentrates on two aspects. The first pertains to Saaty's condition on deleting or combining two alternatives which are ‘near copies’ (alternatives whose priority values are close to each other within a 10% range over all criteria). The second aspect concerns the use of the eigenvector method for estimating the membership values of elements of a fuzzy set. The use of the eigenvector method for estimating fuzzy membership values in a fuzzy set has been justified using the empirical analysis together with theoretical support. It has been amply demonstrated in this paper that the problem lies in Saaty's scale and not in the eigenvector method.