Bayesian inference-based stochastic group priorities acceptability analysis for group decision making with triangular fuzzy preference relations

Triangular fuzzy preference relation (TFPR) is one of the most prevalent tools utilized by decision-makers to express opinions in group decision making (GDM). However, many existing GDM methods with TFPRs not only result in information distortion caused by consistency adjustment but also lead to significant information loss during the integration process. To address these issues, this paper proposes a unique GDM method based on Bayesian inference and stochastic group priorities acceptability analysis, which samples fuzzy preference relations (FPRs) and expert weights using stochastic simulation techniques, and applies the Bayesian inference algorithm to obtain the posterior distribution of group priority vector. First, we establish an additive regression model for a given FPR, and present Bayesian inference algorithms to derive the posterior distribution of priority vector. For GDM with TFPRs, the Bayesian inference-based stochastic group priorities acceptability analysis method, which takes into account the inherent uncertainty in fuzzy preference information, is proposed to obtain the optimal ranking of all alternatives. Additionally, a new framework is constructed to facilitate the computation of descriptive measurements, thereby significantly enhancing the capacity to obtain the optimal ranking. Finally, numerical examples and comparative analysis are employed to demonstrate the applicability and benefits of our proposed method.