Three-way group consensus based on fuzzy social networks under probabilistic linguistic preference relations

Abstract

[EN] The advancement of technology and the rapid developments in the field of artificial intelligence have led to a surge in the research on decision-making in uncertain environments. Furthermore, individual decision-making is too simplistic to solve the complex decision-making problems posed by these challenges, leading to study group decision-making (GDM). Particularly, fuzzy social networks (FSNs) and fuzzy preference relations (FPRs) have important applications in GDM. In addition, probabilistic linguistic term sets (PLTSs) have succeeded as a bridge among natural language, fuzzy reasoning, and probability theory. However, the existing research on GDM under PLTSs faces three key challenges: flaws in PLTSs distance measurement, lack of FSN modeling, and the over-simplified feedback mechanism. These challenges severely impede the effectiveness and reliability of consensus reaching process (CRP) in complex decision-making scenarios. Motivated by these facts, this paper designs a three-way group consensus method based on FSNs under probabilistic linguistic preference relations (PLPRs), namely, the TWD-FSN-PLPR method. This method consists of three successive parts. The first part is the design of an improved consistency method based on the properties of PLTSs. Its main purpose is to ensure that the information on evaluations provided by the decision makers (DMs) maintains internal consistency, paving the way for subsequent GDM. The goal of the second part is to compute the DMs’ weights. Their own familiarity with the PLTS’s cross-entropy and self-confidence are used to construct a directed weighted FSN and then produce the weights from a metric based on social influence. The third part is the consensus reaching process, whose efficiency is improved by a combination of three-way decision and minimum cost, and implementing a penalty mechanism for non-cooperative DMs. In addition, the optimal alternative is selected using regret theory. The methodology is applied to a real case and compared with multiple methods to illustrate its rationality and superiority.