Deriving consistent pairwise comparison matrices in decision making methodologies based on linear programming method

Abstract

Pairwise comparison matrix (PCM) with crisp or fuzzy elements should satisfy consistency requirements when it is used in analytic hierarchy process (AHP) or in fuzzy AHP methodologies. An algorithm has been presented to obtain a new modified consistent PCM for the corresponding inconsistent original one. The algorithm sets a linear programming problem based on all of the constraints. To obtain the optimum eigenvector of the middle value of the new PCM, segment tree is used to gradually approach the greatest lower bound of distance with the original PCM. As to obtain the lower value and upper value of the new PCM, a theory is proposed to reduce adding uncertainty factors and could maximum maintain the similarity with original PCM. The experiments for crisp elements show that the proposed approach can preserve more the original information than references. The experiments for fuzzy elements show that our method can effectively reduce inconsistency and obtain suitable modified fuzzy PCMs. 2014-IOS Press and the authors. All rights reserved.