Stochastic consensus for uncertain multiple attribute group decision-making problem in belief distribution environment

In the realm of uncertain multiple attribute group decision-making (MAGDM) problems, existing research often focuses on the development of consensus-enhancing algorithms grounded in optimization models. However, this paper takes a stochastic perspective, thoroughly considering the impact of uncertainty on decision-making. And a novel stochastic method to model group consensus is introduced with the listed three components: (1) the concept of stochastic rank analysis based on stochastic belief distribution (BD) is given to measure the uncertainty degree in the original BD matrix, which is then used to assign weights to decision makers (DMs). (2) in uncertain environments, to ensure the effectiveness of consensus from a probabilistic perspective, the stochastic consensus index is proposed by taking both the advantages of the Jensen-Shannon (JS) distance and the hesitant distance between stochastic BDs. Then, the expected acceptable group consensus index is further provided to measure the consensus of original preferences among the group, and (3) finally, to deal with the issue of no consensus information, an optimization model is constructed aimed at achieving an acceptable consensus that can generate recommendation advice for DMs, facilitating the attainment of a consensus. The effectiveness of the proposed method is exemplified through two case studies: purchase of new energy vehicles (NEVs) and a postgraduate interview scenario. Furthermore, sensitivity analysis and comparative analysis are presented to better prove its advantages.