A two-stage adaptive consensus reaching model by virtue of three-way clustering for large-scale group decision making

As digitalization advances and societal patterns evolve, an increasing number of experts are becoming integral to the decision-making process. The realm of large-scale group decision making (LSGDM) has gained prominence in management sciences, offering effective solutions for real-world decision challenges. Given that experts from diverse fields possess varying degrees of expertise within LSGDM, their viewpoints exhibit considerable disparity. To attain decision outcomes that enjoy broad consensus, it becomes imperative to ensure equity and rationality within consensus models. However, a significant number of existing consensus models predominantly emphasize inter-subgroup consensus levels, inadvertently neglecting the significance of intra-subgroup consensus degrees. The incorporation of intra-subgroup consensus mechanisms holds pivotal importance for rational subgroup leader selection and opinion refinement among subgroups. Remarkably, this aspect has been underexplored in many prior studies. Addressing this gap, we introduce a novel approach called three-way clustering (TWC), inspired by the traditional k-means clustering technique, denoted as the TWC-KM method. By closely intertwining the clustering process with consensus mechanisms, we introduce a TWC-based two-stage adaptive consensus reaching (ACR) model that judiciously accounts for both intra-subgroup and inter-subgroup consensus aspects, aptly named the TWC-ACR model. Furthermore, we introduce an objective method for setting consensus thresholds, which considers the subgroup silhouette's size. Ultimately, the outcomes of our case study and numerical analysis compellingly demonstrate the superior efficacy and reliability of our devised model.