The large-scale group consensus multi-attribute decision-making method based on probabilistic dual hesitant fuzzy sets

We proposed a novel decision-making method, the large-scale group consensus multi-attribute decision-making method based on probabilistic dual hesitant fuzzy sets, to address the challenge of large-scale group multi-attribute decision-making in fuzzy environments. This method concurrently accounted for the membership and non-membership degrees of decision-making experts in fuzzy environments and the corresponding probabilistic value to quantify expert decision information. Furthermore, it applied to complex scenarios involving groups of 20 or more decision-making experts. We delineated five major steps of the method, elaborating on the specific models and algorithms used in each phase. We began by constructing a probabilistic dual hesitant fuzzy information evaluation matrix and determining attribute weights. The following steps involved classifying large-scale decision-making expert groups and selecting the optimal classification scheme based on effectiveness assessment criteria. A global consensus degree threshold was established, followed by implementing a consensus-reaching model to synchronize opinions within the same class of expert groups. Decision information was integrated within and between classes using an information integration model, leading to a comprehensive decision matrix. Decision outcomes for the objects were then determined through a ranking method. The method's effectiveness and superiority were validated through a case study on urban emergency capability assessment, and its advantages were further emphasized in comparative analyses with other methods.