A decision making model based on the leading principal submatrices of a reciprocal preference relation

Abstract

A completed comparison matrix is the basic tool in the analytic hierarchy process (AHP). In practice, the process of forming a comparison matrix is complex and it is worth being investigated carefully. In this study, by decomposing pairwise comparison process of alternatives, the leading principal submatrices (LPSMs) of a completed comparison matrix are used as the basis for decision analysis. Based on the particle swarm optimization (PSO), a novel method for improving consistency of inconsistent comparison matrices is proposed. The fitness function is constructed by considering the acceptable consistency of pairwise comparison matrices and the similarity degree between the initial and the adjusted decision-making information. A new algorithm is elaborated on for solving a decision making problem with multiplicative reciprocal matrices. Numerical results are reported to show the advantages of the proposed model by comparing with the other methods. The observations reveal that the proposed method and algorithm are effective when dealing with inconsistent comparison matrices and the corresponding decision making problems.