Geometric consistency of triangular fuzzy multiplicative preference relation and its application to group decision making

Abstract

The triangular fuzzy multiplicative preference relation (TFMPR) has attracted the attention of many scholars. This paper investigates the geometric consistency of TFMPR and applies it to group decision making (GDM). Firstly, by introducing two parameters, a triangular fuzzy number is transformed into an interval. According to the geometric consistency of interval multiplicative preference relation (IMPR), the geometric consistency of TFMPR is defined. Then, two corresponding IMPRs are extracted from the TFMPR by programming models in the majority case and minority case, respectively. Using the constructed linear programming models, two interval priority weight vectors are obtained from the two extracted IMPRs, respectively. Combining two interval priority weight vectors, a linear programming model is established to derive the triangular fuzzy priority weights. Subsequently, the closeness degrees of alternatives by experts are defined to obtain the group utility indices and individual regret indices of alternatives. Then, the compromise indices of alternatives are calculated considering experts’ compromise attitude. By minimizing the compromise indices of alternatives, a multi-objective programming model is constructed to obtain experts’ weights. By aggregating the individual TFMPRs, the collective TFMPR is obtained to derive the triangular fuzzy priority weights. Using the arithmetic mean values, the ranking order of alternatives is generated. Therefore, a method is proposed to solve GDM with TFMPRs. Finally, a performance evaluation example of precise poverty alleviation is provided to illustrate the advantage of the proposed method.