Zhen Zhang

During the consensus reaching process (CRP) in large-scale group decision-making (LSGDM) within social networks (SNs), complicated trust relationships and opinion interactions among decision-makers (DMs) may foster opinion polarization, which in turn can trigger non-cooperative behaviors (NCBs) and marginalize minority opinions, thereby undermining consensus efficiency and decision quality. Consequently, effectively managing NCBs and minority opinions is crucial for improving consensus reliability in LSGDM. However, existing studies are still constrained by oversimplified analytical frameworks for NCBs identification, highly subjective approaches to processing minority opinions, and penalty mechanisms that ignore phase-aware adjustments and historical behavioral information. To address these limitations, this paper proposes a consensus model that comprehensively manages NCBs and minority opinions in the CRP. First, a systematic NCB identification framework is developed to distinguish both external and internal NCBs at the subgroup level while also detecting NCBs at the individual level. Second, an objective approach is developed to identify valuable minority opinions, accompanied by a weight-adaptive opinion retention mechanism to ensure due consideration of such opinions. Furthermore, an integrated trust scoring mechanism is introduced to impose differentiated penalties on NCBs across different iteration stages, and a null-norm operator is employed to incorporate DMs’ historical behavioral information for more rational weight updates. Finally, a comparative analysis with existing models is conducted to demonstrate the superiority of the proposed method. A case study on power battery supplier selection demonstrates that the proposed model effectively enhances consensus efficiency while effectively managing both minority opinions and NCBs.

Traditional group decision making (GDM) problems typically aim to obtain a complete ranking of all considered alternatives from best to worst. However, in numerous real-life scenarios, there are instances where it is imperative to assign each alternative into one of two rank levels, creating a ranking where one subset of alternatives is prioritized above the other subset of alternatives. These scenarios are known as 2-rank GDM problems. While a range of methods exist for addressing 2-rank GDM problems, most are specifically tailored to multiattribute decision making situations, thereby limiting their applicability in scenarios involving preference relations. The linguistic preference relation (LPR) is an effective representation tool of decision makers’ (DMs’) preferences for pairwise comparisons of alternatives using linguistic terms. Since words may have different meanings for different DMs, a phenomenon known as personalized individual semantics (PISs), the modeling of linguistic PISs in 2-rank GDM problems with LPRs is worth investigating and challenging to address. Consequently, this article develops models to support consensus reaching for 2-rank linguistic GDM problems with PISs and consistency of DMs. Specifically, PIS consistency-driven models are initially employed to measure and improve the consistency of the LPRs of the individual DMs with unacceptable consistency level. Based on this foundation, the 2-rank vectors for both individuals and the group are determined. Subsequently, a 2-rank consensus measurement method is proposed on which a 2-rank consensus reaching process is designed to support DMs in improving their consensus levels. This involves the development of a PISs-based minimum adjustment consensus optimization model and a PISs-based individual consensus level maximization model. An algorithm to implement the proposed consensus reaching framework is also provided. Finally, numerical experiments and simulation results are reported to demonstrate the effectiveness of the proposed method.

The density peaks clustering (DPC) algorithm has attracted considerable attention for its ability to detect arbitrarily shaped clusters based on a simple yet effective assumption. Recent advancements integrating granular-ball (GB) computing with DPC have led to the GB-based DPC (GBDPC) algorithm, which improves computational efficiency. However, GBDPC demonstrates limitations when handling complex clustering tasks, particularly those involving data with complex manifold structures or non-uniform density distributions. To overcome these challenges, this paper proposes the local GB quality peaks clustering (LGBQPC) algorithm, which offers comprehensive improvements to GBDPC in both GB generation and clustering processes based on the principle of justifiable granularity (POJG). Firstly, an improved GB generation method, termed GB-POJG+, is developed, which systematically refines the original GB-POJG in four key aspects: the objective function, termination criterion for GB division, definition of abnormal GB, and granularity level adaptation strategy. GB-POJG+ simplifies parameter configuration by requiring only a single penalty coefficient and ensures high-quality GB generation while maintaining the number of generated GBs within an acceptable range. In the clustering phase, two key innovations are introduced based on the GB k-nearest neighbor graph: relative GB quality for density estimation and geodesic distance for GB distance metric. These modifications substantially improve the performance of GBDPC on datasets with complex manifold structures or non-uniform density distributions. Extensive numerical experiments on 40 benchmark datasets, including both synthetic and publicly available datasets, validate the superior performance of the proposed LGBQPC algorithm.