Rectifying the Inconsistent Fuzzy Preference Matrix in AHP Using a Multi-Objective BicriterionAnt

Abstract

Analytic hierarchy process (AHP) is a decision making tool regarding the criteria analysis to obtain a priority alternative. One of the important issues in comparison matrix of AHP is the consistency. The inconsistent comparison matrix cannot be used to make decision. This paper proposes an algorithm using a modified BicriterionAnt to pursue two objectives intended to rectify the inconsistent fuzzy preference matrix, called MOBAF. The two objectives include minimizing the consistent ratio (CR) and minimizing the deviation matrix, which are in conflict with each other when rectifying the inconsistent matrix. This study uses two pheromone matrices and two heuristic distances matrices to generate the ants tour. To see the performance, MOBAF is implemented to rectify on some inconsistent fuzzy preference matrices. As a result, in addition to being able to rectify the CR, the proposed algorithm also successfully generates some non-dominated solutions that can be considered as optimal solutions.