Consistency of pairwise comparison matrices focusing on pairwise comparison values among three items and Saaty’s Consistency Index (C.I.) :Indentifying inconsistent pairwise comparison values using transitivity and relaxed consistency constraints

Abstract

The Consistency Index (C.I.) has been mainly used as a consistency index for the pair-wise comparison matrix of the Analytic Hierarchy Process (AHP). In order to improve the pairwise comparison matrix, modifications have been made based on the difference between the ratio of importance calculated by the eigenvalue method and the pairwise comparison value. In this paper, we focus on the pairwise comparison values between any three items of the evaluation criteria, and obtain more accurate importance values by modifying them to satisfy transitivity, relaxed consistency constraints, and consistency constraints, or by modifying the correspondence table between the pairwise comparison words and the values.