A large-scale group decision-making approach based on hesitancy degrees and non-cooperative behaviors with picture fuzzy information

Large-scale group decision-making (LSGDM) problems involve two processes: a clustering process is first implemented to break down a larger group into several smaller subgroups for simplification purposes, after which a consensus reaching process (CRP) is utilized to eliminate information conflicts among large-scale decision-makers (DMs). Opinion conflicts are inevitable in large DM groups due to self-interest biases and information blind spots. To address these limitations, this study proposes a twofold feedback mechanism to address both non-cooperative behaviors and information hesitation. Firstly, based on detailed review of existing similarity measures, we defined a novel picture fuzzy Chi-square similarity measure (NPFCS) to enhance accuracy. To distinguish subgroups, the second procedure was developed to establish a weight assignment model following the implementation of the developed similarity-based fuzzy clustering algorithm. In the third step, decision opinions are examined from two distinct perspectives: the hesitancy degrees and non-cooperative behaviors, to ensure favorable decision outcomes. Alongside the definition of a hierarchical mechanism for detecting DMs with information blind spots, the identified DMs were mandated to resubmit individual matrices. This measure aims to prevent the aggregation of negative impacts on information credibility caused by the major principle. Furthermore, non-cooperative behaviors were identified at the element level of multi-criteria matrices with corresponding adjustments performed automatically. Next, a real-world site selection problem involving thirty DMs was solved using the proposed method to illustrate its application. Moreover, the results of sensitivity analysis demonstrate that our proposal is robust to changes in model parameters, and several comparisons were conducted from two perspectives, thus confirming the superiority of the proposed approach.