A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters

In the large-scale group decision making (LGDM) consensus process, it is usually assumed that the obtained clusters do not change. However, as the individual preferences change as part of the decision process, this is generally not the case. The aim of this paper, therefore, is to propose a LGDM consensus model in which the clusters are allowed to change and the decision makers provide preferences using fuzzy preference relations. The most commonly used clustering method, k-means, is introduced to identify the subgroups and a possibility distribution based hesitant fuzzy element (PDHFE) is employed to represent each cluster preference. A novel distance measure over the PDHFEs is given to compute the various consensus measures, after which a local feedback strategy with four identification rules and two direction rules is designed to guide the consensus reaching process. The proposed model is distinguished from previous studies where the changes occur on the obtained clusters that the feedback mechanism is directly based on the decision makers in the identified clusters. Further, as the clusters (virtual or nominal) change in every interactive consensus round, the consensus process evolution can be captured. Finally, an emergency decision to choose a rescue plan is illustrated to validate the proposed method and demonstrate distinctive characteristics compared with the existing approaches.