AConsistency-Driven Group Decision Making Approach with Triangular Fuzzy Reciprocal Preference Relations

Abstract

Triangular fuzzy reciprocal preference relations (TFRPRs) are one of the effective tools for expressing the fuzzy and uncertain preferences of decision makers in group decision making. The consistency of TFRPRs is a key prerequisite for reasonable and reliable de cision making. To this end, this study developed an improved multiplicative acceptable consistency group decision-making method based on TFRPRs. By analyzing the compo sition of TFRPRs, the multiplicative consistency index and the corresponding threshold are defined to measure whether TFRPRs have acceptable consistency. This consistency measure reflects the essential characteristics of triangular fuzzy numbers and fully consid ers the multiplicative consistency of the mode value and the multiplicative consistency of the geometric mean based on the central tendency. Then, three inconsistent TFRPR cases are analyzed, and an algorithm for solving TFRPR inconsistency based on mathematical derivation and linear programming model is proposed. Based on the multiplicative accep tance consistency (MACD) of TFRPRs, a MACD-IOWA is proposed to aggregate individ ual TFRPRs into group TFRPRs. The basic principle is that the higher the MACD value, the higher the decision maker’s weight. Finally, the feasibility and effectiveness of the proposed method are verified through case studies, comparative analysis and discussion.