Construction of consistent comparison matrix by Macharis' method revisit

Abstract

A famous paper that has been cited more than four hundred times tried to combine (a) the preference ranking organization method for enrichment evaluations (PROMETHEE) and (b) the analytic hierarchy process (AHP) to construct a new method for multicriteria decision-making problems. The paper developed a consistent comparison matrix for their AHP by the defined first row and then they allowed the expert to change several entries in the comparison matrix. Hence, how to construct a new comparison matrix that is (i) consistent and (ii) satisfying the assigned values by the expert becomes a challenging problem. A recent article provided a reply to the above problem by the construction of all entries for the comparison matrix. However, they did not follow the original design proposed by the famous paper. In this paper, we present a new approach with a proposition that satisfies the original design of the famous paper and also achieves two goals (i) and (ii). The research gap of proof is fulfilled by this paper. Our findings explain that the original construction of the famous paper to develop a consistent comparison matrix only by the first row with several assigned values by an expert is indeed workable under two additional restrictions proposed by the recent article. We believe that after our proposition, researchers have the confidence to execute the original design of the paper that has been cited more than four hundred times.