An optimization-based method for eliciting priorities from fuzzy preference relations with a novel consistency index

Preference relations could be originated from a decision making problem by pairwisely comparing a finite set of alternatives. In order to find an optimal solution, a feasible approach is to elicit the priorities from the derived preference relation. In this paper, we report an optimization-based approach to the priorities elicited from fuzzy preference relations (FPRs). The inherent relation between row/column vectors of FPRs with additive/multiplicative consistency is considered. Under additive consistency, the variance-based additive consistency index (VACI) of FPRs is constructed and some properties are studied. With the knowledge of multiplicative consistency, the concept of transformation-based multiplicative consistency index is proposed. Using numerical simulations, the thresholds of the proposed consistency indexes for FPRs with acceptable additive/multiplicative consistency are determined. A new method for deriving the priority vector from FPRs is proposed by constructing an optimization problem. The optimal solution is studied and some comparisons with the existing methods are made. Finally, numerical examples are carried out to show the effectiveness of the proposed approach.