Building Consensus with Enhanced K-means++ Clustering: A Group Consensus Method Based on Minority Opinion Handling and Decision Indicator Set-Guided Opinion Divergence Degrees

The complexity of large-scale group decision-making (LSGDM) in the digital society is becoming increasingly prominent. How to achieve efficient consensus through social networks (SNs) has become a core challenge in improving the decision quality. First, conventional clustering methods often rely on a single-distance metric, neglecting both numerical assessments and preference rankings. Second, ensuring the decision authenticity requires considering diverse behaviors, such as trust propagations, risk preferences, and minority opinion expressions, for scientific decision-making in SNs. To address these challenges, a consensus-reaching process (CRP) method based on an enhanced K-means++ clustering is proposed. The above method not only focuses on minority opinion handling (MOH), but also incorporates decision indicator sets (DISs) to analyze the degree of opinion divergences within groups. First, the Hamacher aggregation operator with a decay factor completes trust matrices, improving the trust representation. Second, a personalized distance metric that combines cardinal distances with ordinal distances is incorporated into the enhanced K-means++ clustering, enabling more precise clustering. Third, weights for decision-makers (DMs) and subgroups are determined based on trust levels and degree centrality indices. Fourth, minority opinions are appropriately handled via considering the diverse backgrounds and expertise of DMs, leveraging a difference-oriented DIS to detect and adjust these opinions via weight modifications until a consensus is reached. Fifth, the alternative ranking is objectively generated via DIS scores derived from multigranulation rough approximations. Finally, the feasibility of the proposed method is validated via a case study on unmanned aerial vehicle (UAV) selection using online reviews, supported by a sensitivity analysis and comparative experiments demonstrating superior performances over existing methods. The result shows that the proposed model can enhance clustering accuracies with hybrid distances, objectively measure the consensus via DISs, handle minority opinions effectively, and improve LSGDM’s overall efficiencies.