An improved multiplicative acceptability consistency-driven group decision making with triangular fuzzy reciprocal preference relations

Triangular fuzzy reciprocal preference relation (TFRPR) is one of the most effective tools to express the vague and uncertain preferences of decision makers in group decision making (GDM). Consistency of TFRPRs is a crucial premise for reasonable and reliable decision-making. To do so, this study develops an improved multiplicative acceptability consistency-driven GDM with TFRPRs. By analyzing the composition of TFRPRs, a multiplicative consistency index and the corresponding threshold are defined to measure whether a TFRPR is acceptably consistent. The consistency measurement reflects the essential traits of triangular fuzzy numbers, which fully considers the multiplicative consistency of modal values and the multiplicative consistency of geometric mean based on central tendency. Subsequently, three inconsistent TFRPR cases are analyzed, and the algorithm based on mathematical derivation and a linear programming model is presented to repair the inconsistency of TFRPRs. As per the multiplicative acceptability consistency degree (MACD) of TFRPRs, an MACD-induced ordered weighted averaging (MACD-IOWA) operator is proposed to aggregate individual TFRPRs into group TFRPR. The essence principle is that the larger the MACD value, the higher the decision maker's weight. Finally, a case study, comparative analysis and discussions are given to verify the feasibility and validity of the proposed methods.