Bayesian revision of the individual pair-wise comparison matrices under consensus in AHP–GDM

Abstract

Analytic hierarchy process (AHP) has been widely used in group decision making (GDM). There are two traditional aggregation methods for the synthesis of group priorities in AHP–GDM: aggregation of the individual judgments (AIJ) and aggregation of the individual priorities (AIP). However, AIJ and AIP may be less reliable because of inconsistency of the individual pair-wise comparison matrices (PCMs) and deviation among decision makers. Based on multiplicative AHP model with lognormal errors, we propose a Bayesian revision method for improving the individual PCMs under the assumption that the consensus exists among decision makers, which is considered an aid to AIJ and AIP. In order to effectively deal with decision making involving multiple actors when using AHP as the methodological support, we revise the individual PCMs using the Bayesian revision method before using AIJ and AIP for the synthesis of group priorities. The Bayesian revision method not only makes full use of the prior distribution for parameters and sample information while complying with the Pareto principal of social choice theory, but also provides the reliable individual Bayesian PCMs for AIJ and AIP. Finally two numerical examples are examined to illustrate the applications and advantages of the Bayesian revision method.