Pairwise opposite matrix and its cognitive prioritization operators: comparisons with pairwise reciprocal matrix and analytic prioritization operators

Abstract

The pairwise reciprocal matrix (PRM) of the analytic hierarchy/network process has been investigated by many scholars. However, there are significant queries about the appropriateness of using the PRM to represent the pairwise comparison. This research proposes a pairwise opposite matrix (POM) as the ideal alternative with respect to the human linguistic cognition of the rating scale of the paired comparison. Several cognitive prioritization operators (CPOs) are proposed to derive the individual utility vector (or priority vector) of the POM. Not only are the rigorous mathematical proofs of the new models demonstrated, but solutions of the CPOs are also illustrated by the presentation of graph theory. The comprehensive numerical analyses show how the POM performs better than the PRM. POM and CPOs, which correct the fallacy of the PRM associated with its prioritization operators, should be the ideal solutions for multi-criteria decision-making problems in various fields.

Keywords:

• decision analysis
• utility theory
• analytic hierarchy/network process (AHP/ANP)
• cognitive decision system
• optimization

Acknowledgements

The research work is essentially derived from the author's PhD thesis, The Hong Kong Polytechnic University. Thanks are also extended to the anonymous referees for their time and effort to improve the work.