Group decision making (GDM) problems with interval multiplicative preference relations (IMPRs) contain uncertain preference information from the decision makers (DMs). To help the DMs make decision quickly and accurately, this article proposes a novel framework to GDM problems with IMPRs by combining the ELECTRE III method with stochastic simulation. First, the stochastic multiplicative preference relations are derived by stochastic simulation, then the individual stochastic priority vector and the group stochastic priority matrix are defined. Second, the group stochastic net credibility degree is presented to evaluate all alternatives. Third, several optimal group measurements are proposed, including the group stochastic rank acceptability degree, the optimal preference rank, the group stochastic central weight vector, and the group stochastic optimal confidence factor. Moreover, a novel framework for GDM problems with IMPRs is put forward by using the stochastic simulation with the ELECTRE III method. The proposed approach retains the initial opinions of DMs and reduces the influence of DMs’ subjectivity, besides considers the ranking possibility of all alternatives from an expected perspective. Finally, a medicine decision example of Wilson disease is analyzed, comparison analysis and sensitivity analysis are conducted to verify the validity and feasibility of the proposed approach.

In traditional social network analysis-based group decision-making problems, decision makers (DMs) commonly establish trust relationships with unfamiliar DMs based on the transitivity of trust but always ignore the effectiveness of such indirect trust and the potential risks that may arise from excessive trust/distrust. To overcome this limitation, this paper explores a Bayesian framework to construct trust relationships among a group which can update the direct trusts between DMs by considering the trusts to the trustee from other DMs trusted by the original trustor. The Bayesian trust relationship can not only supplement the incomplete trust relationships based on known trust information, but also make reasonable adjustments to existing trusts before the decision process. And it has been proven to be effective in mitigating inaccuracies in decision outcomes resulting from either excessive trust or distrust, and in reducing information loss caused by excessively long paths during trust transition. Relatedly, after giving the algorithm of the Bayesian trust relationship, the rank discrepancy between DMs is defined in uncertain belief distribution environment to measure and constrain the trust decision indicator (TDI) in the Bayesian framework. Then, constrained by expected rank discrepancy, the stochastic TDI analysis is introduced to derive the confidence weight intervals of DMs. And an optimization model is provided to maximize the group consensus within the constraints of the generated interval weights. Finally, a case study of new energy vehicles selection is presented. Additionally, both comparative study and sensitivity analysis are provided.