Social network group decision-making for probabilistic linguistic information based on GRA

In group decision-making problems, decision-makers typically use probabilistic linguistic term sets (PLTSs) to express their evaluation opinions. This paper focuses on the social network group decision-making method for probabilistic linguistic information. First, we propose a new consensus judgment mechanism by computing the absolute grey relation degree between the most probable optimal vectors of individual decision makers and collective opinion. Furthermore, in order to reduce the calculated amount in the decision-making process, we propose a model to transform the score value into a PLTS. This technique uses stochastic multicriteria acceptability analysis to determine the criteria weights. The preferences of the decision-makers can be accurately portrayed by this approach. In addition, we put forward a model to transform the score value into a PLTS and propose a new way to obtain the criteria weights using stochastic multicriteria acceptability analysis. Moreover, we develop an advice generation method with two steps for the PLTS in a feedback adjustment process. Finally, we use a case study and comparative analysis to illustrate the effectiveness of our method. Our proposed method can be applied to address many group decision-making problems involving multiple interest groups, such as social policy, facility placement, and other issues.