Measuring inconsistency and deriving priorities from fuzzy pairwise comparison matrices using the knowledge-based consistency index

摘要

The fuzzy analytic hierarchy process (AHP) is a widely applied multiple-criteria decision-making (MCDM) technique, making it possible to tackle vagueness and uncertainty arising from decision makers, especially in a pairwise comparison process. Indeed, as the human brain reasons with uncertain rather than precise information, pairwise comparisons may involve some degree of inconsistency, which must be correctly managed to guarantee a coherent result/ranking. Several consistency indexes for fuzzy pairwise comparison matrices (FPCMs) have been proposed in the literature. However, some scholars argue that most of these fail to be axiomatically grounded, which may lead to misleading results. To overcome this lack of an axiomatically grounded index, a new index is proposed in this paper, referred to as theknowledge-based consistency index(KCI). A comparative study of the proposed index with an existing one is carried out, and the results show that KCI contributes to substantially reducing the computation time. In addition, the different fuzzy weights derived from the initial FPCM (for KCI computation purposes) can also be employed to find a crisp set of weights that corresponds to an optimal solution to the MCDM problem according to the decision maker’s viewpoint and expertise.