Deriving the priority weights from trapezoidal fuzzy reciprocal preference relations based on uncertainty ratio and geometric mean

Abstract

Trapezoidal fuzzy reciprocal preference relation (TraFRPR), whose elements are trapezoidal fuzzy numbers, is a powerful tool to simulate the pairwise comparison judgments with imprecision and vagueness. How to define the consistency and derive the priority weights are two important research topics for decision making with TraFRPRs. This paper will focus on solving these two issues. The paper analyzes the existing definitions of consistent TraFRPRs and concludes that they are flawed by not being robust to permutations of the DM’s judgments. A new trapezoidal fuzzy arithmetic based consistency definition is proposed for TraFRPRs, and properties of consistent TraFRPRs in light of the new definition are studied in detail. An acceptably consistent TraFRPR is then defined. A geometric mean and uncertainty ratio based transformation formula is put forward to convert a normalized trapezoidal fuzzy multiplicative weight vector into a consistent TraFRPR. A logarithmic least square model is developed to derive a normalized trapezoidal fuzzy multiplicative weight vector from an acceptably consistent TraFRPR and to construct the fitted consistent TraFRPR. A numerical example is given to illustrate the validity and applicability of the proposed models.