Managing non-cooperative behaviors is a critical challenge in the consensus reaching process of large-scale group decision-making (LSGDM). Existing studies usually rely on static social relationships and non-overlapping community structures, which cannot adequately capture the dynamic interactions and multiple community memberships of decision experts. To address this issue, this study proposes a consensus model that fuses dynamic social network relationships and overlapping community structures for non-cooperative behavior management in LSGDM. Firstly, the COPRA algorithm is used to cluster decision experts and effectively identify experts and communities with overlapping structures, thus capturing the complex social interaction patterns among decision experts. Secondly, the PageRank algorithm is used to calculate the weights of decision experts based on the social network structure. On this basis, a consensus model is constructed by fusing dynamic network relationships and overlapping communities, which guides experts to adjust their opinions through feedback mechanisms, thereby reducing the influence of non-cooperative behaviors and promoting consensus reaching. To verify the rationality of the proposed method, the model is applied to a subway line planning decision problem. Finally, simulation experiments and comparative analyses demonstrate that the proposed method is effective in managing non-cooperative behaviors and improving consensus performance compared with existing approaches.

This paper proposes a two-stage integrated model to compare the effectiveness of proactive strategies (PSs) for mitigating supply chain disruptions from a risk-averse perspective. First, factors influencing the effectiveness of PSs are analyzed, with supply and demand uncertainties characterized using a scenario-based method and a Markov chain model, respectively. Second, a novel two-stage integrated model is developed, which aims to minimize the expected worst-case costs through the Conditional Value-at-Risk approach. Finally, the model is validated through numerical examples, including comparison and sensitivity analyses to assess the effectiveness of single and combination of PSs in addressing potential disruption risks. The results indicate that: (1) the performance of PSs, or their combinations, varies according to the manufacturer's level of risk-aversion. At high levels of risk-aversion, the benefits of combined PSs become increasingly significant; (2) the effectiveness of combined strategies is not always superior to that of single-PS. Indeed, a strategy that generally performs poorly can contribute to an effective combination, and vice versa, due to interactions among different strategies; and (3) the effectiveness of PSs is influenced by several factors, with risk-aversion, demand state transition, and pre-disruption budget being critical determinants. This study provides valuable insights for manufacturers' supply chain risk management.

Modern complex systems often feature multiple output dimensions, making it essential to evaluate efficiency across these diverse outputs. This study introduces a joint neutral cross efficiency evaluation mechanism designed specifically for multiple output dimensions. The mechanism addresses the issue of zero weights by incorporating a minimum weight constraint and formulates an objective function based on a maximization-minimization criterion to reduce efficiency discrepancies. It integrates prospect theory to reflect decision-makers' preferences regarding efficiency deviations and iteratively generates a consistent cross-efficiency matrix aggregation scheme. In comparison with traditional methods, the proposed mechanism employs a unified reference set, ensuring comparability of results across different dimensions. It enhances the coordination and consensus of cross-evaluations across different output dimensions. To illustrate its effectiveness, the mechanism is applied to assess the forestry efficiency of 31 provinces in China. The results indicate two distinct patterns of development: coordinated development across output dimensions and uncoordinated development.

Emergency plans are an indispensable component of emergency management, designed to effectively handle critical situations when an emergency event occurs. Due to its significance and necessity, emergency planning has drawn increasing attention in recent years. A central focus in this area is how to generate emergency plans effectively and adaptively. Numerous studies have approached this challenge from various perspectives, obtaining valuable insights and outcomes. Dynamic evolution and uncertainty are two pivotal, practical factors that emerge during emergency events and must be carefully considered in the generation of effective emergency plans. However, existing studies have not sufficiently tackled these critical aspects. To bridge this gap, this study proposes a robust optimization-based emergency plan generation method, which accounts for dynamic evolution by incorporating timeline changes, shifts in emergency situations, and updates in available resources. Additionally, it systematically integrates uncertainty from both quantitative and qualitative perspectives. Finally, an illustrative example, along with related discussions and comparisons, is provided to demonstrate the feasibility, validity, and contributions of the proposed method.

The frequent emergencies often lead to significant human and material losses, creating urgent and complex logistical demands. One of the key tasks in emergency logistics is the selection of a suitable site for constructing an emergency logistics center to facilitate timely relief delivery. To support the complex decision-making process involved in emergency logistics center site selection, this study proposes a multi-criteria group decision-making method that effectively handles uncertainty and hesitation in expert evaluations. Specifically, we propose an extended ORESTE (organisation, rangement et Synth & egrave;se de donn & eacute;es relarionnelles, in French) method integrated with normal-type hesitant fuzzy sets (N-HFSs). While the traditional ORESTE method is valued for its simplicity and capability for conflict analysis, it suffers from information loss and lacks flexibility in representing hesitant preferences. To address these limitations, N-HFSs are employed to more accurately reflect expert hesitation, and a new position-based distance measure is introduced to compare N-HFSs without requiring normalization, thus avoiding computational bias and enhancing interpretability. Moreover, an improved version of the ORESTE method is proposed in this paper to address the drawback of information losses. The proposed approach is applied to a case study involving the selection of emergency logistics center sites in China. Finally, to validate the robustness and effectiveness of the proposed method, comparative and sensitivity analyses are conducted. This model provides actionable guidance for emergency-management authorities and demonstrates that the new decision framework is a reliable tool for high-stakes, uncertain group decisions.

Sorting problem has become one of the most common Multi-Criteria Decision-Making (MCDM) problems in real-life scenarios. In classical multi-criteria sorting methods, the input data are required to be precisely expressed by quantitative and crisp values. However, due to the inherent uncertainty of real-life problems, crisp values may not be enough to model the decision information. In addition, while multi-criteria sorting methods often utilize group intelligence, they seldom address the challenges of Consensus Reaching Processes (CRP) as non-cooperative behaviors or human bounded rationality, in spite of they are common challenges in MCDM. In such a context, this paper develops a novel multi-criteria sorting method to model the uncertainty, manage the CRP as well as capture the human bounded rationality, and then obtain better decision solutions by considering these issues. An illustrative numerical example is presented to demonstrate the effectiveness and applicability of the proposed method. The results highlight the potential of the proposed method in addressing the multi-criteria sorting problems with uncertain and imprecise input information under bounded rationality hypothesis. Comparative analysis and sensitivity analysis are also conducted to show the advantages and robustness of the current proposal, respectively.

This paper proposes a new consensus-reaching method for group decision-making with dynamic adjustment costs. In practice, group members often disagree and are reluctant to revise their opinions unless they are adequately compensated. Moreover, consistent with the law of diminishing marginal utility, the benefit derived from each additional unit of opinion adjustment tends to decrease over time. To capture different dynamic patterns of adjustment costs, four mathematical functions, namely linear, power, exponential and logarithmic functions, are introduced into the group consensus-reaching process. Based on these functions, a flexible adjustment cost mechanism is developed to guide opinion modification. Considering the asymmetry of adjustment costs, that is, the costs of increasing and decreasing opinions may differ, this study further extends the framework to accommodate asymmetric adjustment cost structures. To support function selection and clarify the characteristics of different specifications, several decision rules are derived and validated through illustrative examples. In addition, extensive numerical experiments and detailed discussions are conducted to demonstrate the effectiveness and advantages of the proposed method. The results show that different functional forms of adjustment costs can lead to substantially different decision outcomes, highlighting the importance of capturing the dynamic evolution of adjustment costs in group consensus.

Best-Worst Method (BWM) is a behaviorally-inspired decision-making method supporting decision-makers to evaluate and prioritize alternatives based on a set of criteria. This study introduces a novel version of BWM, incorporating concepts from the FlowSort method, which is designed to classify alternatives. Given a set of alternatives characterized with a number of criteria, first, a set of limiting profiles, as multi-criteria vectors, is defined by the decision-maker. Using these limiting profiles, pairwise comparisons are conducted between the two reference limiting profiles (best and worst), and the other limiting profiles. These pairwise comparisons form the basis to derive the priorities of the limiting profiles, which are the foundation of establishing criterion-specific value functions. Then, the criterion-wise value scores of alternatives are derived from the value functions. Subsequently, the outranking degrees between alternatives and reference limiting profiles are calculated based on a V-shape function. Following this, a min–max optimization model is established to infer classification indices. Finally, by exploring the relationships between classification indices of limiting profiles and alternatives, several assignment rules are developed to classify alternatives into different classes. The proposed method is applied to a supplier classification problem, and its performance is compared with several existing multi-criteria sorting methods. Its practical applicability is further demonstrated through a real-world case study on university assessment.

The Extended Belief Rule Base (EBRB) serves as a rule-based decision-making system and has been widely applied in classification tasks due to its interpretability and transparency. However, it faces issues of low reasoning efficiency and limited modeling capability when dealing with highdimensional nonlinear data. Previous approaches have improved EBRB by constructing rule indexes and introducing neural network algorithms. Nevertheless, these methods still suffer from overly local aggregation of rule information and instability of the constructed graph structure. To address these issues, we propose an EBRB system optimized based on clustering graph structure and Graph Transformer (GT-EBRB). Specifically, GTEBRB first performs rule clustering on the rule base, employing the Silhouette Coefficient to filter out noisy rule nodes. Subsequently, a probability-based edge connection strategy is designed to capture and represent a more global rule community structure, modeling a more stable clustering graph structure for the rule base. Given that Graph Transformer possesses self-attention mechanisms and global information aggregation capabilities, we thus propose integrating the Graph Transformer algorithm with rule positional encoding for rule representation learning and generating activation weights for rules. Moreover, sparse evidential reasoning is adopted in the inference phase to further enhance inference efficiency and the consistency of activated rules. We conducted comprehensive experiments on 11 UCI classification datasets, and the results demonstrate the superior classification performance of GT-EBRB.

Large-scale group decision-making (LSGDM) represents a pivotal methodology for addressing complex problems involving a multitude of decision-makers (DMs), wherein social relationships—particularly trust—among DMs substantially drive the decision outcomes. Existing trust propagation techniques frequently depend on nodes whose reliability is uncertain, thereby potentially establishing trust links that lack empirical validity, while also overlooking the dynamic development of trust relationships. Furthermore, traditional consensus frameworks often exhibit deficiencies in effectively managing outliers and dynamically adapting DM weights, which undermines both the reliability and fairness of consensus results. To address these deficiencies, this study proposes an integrative LSGDM framework grounded in the minimum adjustment consensus model (MACM), which synergistically incorporates a trust development model based on familiarity and reliability metrics, a trust-embedded affinity propagation clustering algorithm, and a multi-stage dynamic weight adjustment mechanism informed by robust statistical outlier detection methods. Additionally, a dynamic bounded confidence adjustment strategy is introduced to attenuate the influence of outliers while preserving the integrity of individual subjective judgments. This holistic approach facilitates efficient consensus achievement with minimum opinion adjustments, and strengthens the robustness of group opinion aggregation. The validity and superiority of the proposed methods are substantiated through comprehensive case studies and simulation experiments.

Coordinating upstream-downstream decisions in supply-chain systems is essential for efficient resource allocation and overall performance. Yet relatively little work examines how purposeful reconfiguration of network structure can raise end-to-end efficiency. To address this gap, we study a two-stage supply-chain network within the network data envelopment analysis (NDEA) paradigm and integrate NDEA with strategic structural-reconfiguration methods. We develop a permutation-game-theoretic framework to optimize subsystem configurations under three decision control modes - centralized, decentralized, and hybrid control. Using an empirical case study, we validate the approach and show that it effectively uncovers vertical synergies between upstream and downstream entities. The results indicate that structural adjustments guided by our framework can enhance overall operational efficiency.

In large-scale group decision-making (LSGDM), directly establishing trust relationships among decision-makers (DMs) is challenging due to the influence of multiple factors. Moreover, DMs typically prioritize achieving their own goals when adjusting their opinions. Existing studies fail to identify the sources of trust, tending to rely on single-factor analyses. In real-world decision-making environments, decision-making groups often adopt a certain approval proportion to determine whether consensus on a solution has been achieved, depending on the nature of the decision problem. Requiring agreement from all DMs frequently leads to excessive communication and coordination efforts, which in turn reduces decision-making efficiency. To address these limitations and better reflect real-world decision-making processes, this paper proposes a minimum adjustment consensus model (MACM) for LSGDM based on a hybrid trust network. The method consists of three stages. Firstly, to obtain more accurate trust relationships, a hybrid trust network is constructed by integrating expert collaboration and opinion similarity. Second, based on the hybrid trust network and the consistency of alternative rankings, an improved Louvain algorithm is applied to identify multiple subgroups. Finally, an MACM considering consensus proportion and rules is proposed. An example of urban public transportation system optimization is provided for application analysis and comparison. The results demonstrate that the proposed method is both feasible and effective.

Extreme weather-induced flooding poses significant threats to urban safety and public health. The complexity of emergency alternative selection faced by disaster management authorities intensifies crisis resolution challenges. Optimal resource allocation and prioritized response strategies constitute core components of disaster management, where flood emergency alternative evaluation emerges as a quintessential Multi-Attribute Group Decision-Making (MAGDM) problem, directly impacting the timeliness and effectiveness of emergency response efforts. In this paper, a novel probabilistic hesitant fuzzy TODIM (an acronym in Portuguese for Interactive Multi-Attribute Decision-Making) method is proposed to optimize emergency response. To address the absolutization present in existing studies, a new score function grounded in prospect theory is devised to solve probabilistic hesitant fuzzy sets (PHFSs) by interpreting the probabilistic characteristics. Subsequently, by combining with the maximum deviation method, an attribute weight determination model is introduced. Besides, probabilistic hesitant fuzzy Wasserstein similarity measure is constructed and an expert weight determination approach is designed on this basis. Furthermore, the specific steps of the novel TODIM method are introduced. As a critical component of the TODIM method, the loss aversion coefficient is derived through a grey relational analysis-based approach, aiming to reflect risk psychology of decision-makers (DMs) through the correlation of evaluation information. By applying the method to emergency alternative selection for the urban flood disaster in Zhengzhou, its feasibility is demonstrated. Simulation analysis and comparison analysis with existing methods demonstrate the feasibility and practicality of the proposed method.

The proliferation of retired electric vehicle batteries presents a significant threat to environmental and resource sustainability, necessitating collaborative efforts among supply and recycling chain actors. This study examines how coalition cooperation among actors can enhance the recycling of electric vehicle batteries, thereby improving both economic and environmental performance. Specifically, we utilize non-cooperative game theory to analyse five cooperative strategies in a tripartite closed-loop supply chain involving an electric vehicle manufacturer, a retailer, and a third-party recycler. We also scrutinize the effects of joint recycling regulation and carbon policy, i.e., reward-penalty and cap-and-trade mechanisms, on supply chain operations. The findings indicate that augmented external environmental pressures, in addition to enhancing collection rates, may bolster the supply chain’s economic yield under specific scenarios. While cooperative strategies led by an electric vehicle manufacturer exhibit potential for superior economic viability or heightened environmental sustainability, the formation of partial coalitions within the supply chain could result in an unequal distribution of profits. We employ cooperative game theory, specifically the Shapley value, to implement a fair profit allocation mechanism aimed at fostering cooperation and coordination within the supply chain.

Trust relationships are crucial for reaching consensus in the field of large-scale group decision making (LSGDM). They also serve as the basis for expert interactions and have a significant impact on important aspects like determining the importance of experts and modifying preference information. Research on LSGDM that takes trust into account rarely examines how preference information and trust interact or how trust affects bounded confidence models. As a result, this study suggests a novel LSGDM model that incorporates dynamic trust relationships and limited confidence into the hybrid social network. First, a trust evaluation method based on preference similarity is proposed. Next, the improved hierarchical clustering algorithm is utilized to cluster the asymmetric hybrid social network and determine the weight indices. Subsequently, a dual-driven trust evolution mechanism and a bounded confidence model incorporating trust relationships are proposed. Then, the feasibility of the model is tested through simulation experiments and a practical case involving unmanned mining truck supplier selection in a mining group. Finally, the effectiveness and superiority of the model are demonstrated by comparison with existing methods.

With the development of the Internet, online reviews have become an indispensable reference in decision-making processes. As a prevalent social behavior, group decision-making (GDM) is widely applied across various domains. Integrating valuable information from online reviews with GDM not only bridges real-world applications through authentic data but also significantly enhances decision accuracy and reliability. However, members’ preferences in GDM are fuzzy and conflicting, making consensus achievement critical for opinion coordination. This paper proposes an online review-driven group consensus decision-making method based on sentiment analysis and an adaptive feedback model. The method transforms online reviews into attribute-level sentiment scores, uses a novel Precise-Interval Fuzzy Preference Relation (PIFPR) structure to objectively extract endo-confidence, determines influence weights by fusing subjective and objective factors, and implements an adaptive feedback mechanism with tailored adjustment strategies. Using TripAdvisor hotel selection as a case study, the method’s practical feasibility is demonstrated. Simulation experiments show that preference adjustment cost is reduced by over 9.9

The core of evidence theory is the combination algorithm, which can be divided into two categories: the recursive combination algorithm and the analytical combination algorithm. While the former has been extensively developed, its calculation process requires constant iterations, which makes it difficult to use in certain situations, such as problem optimization. The latter can obtain the final fusion result through one-step calculation; however, it has attracted little attention, and there are still some limitations to be overcome, such as its neglects of reliability and poor handling of local ignorance. This study constructs an analytical generalized combination (AGC) rule for evidence. We propose an AGC rule as an analytical form without iteration to directly fuse multiple pieces of evidence with both weight and reliability. A series of theorems and corollaries are established to demonstrate its effectiveness. We analyze the properties of the AGC rule by clarifying its relationship with existing analytical combination algorithms (i.e., the analytical ER algorithm and general analytical interval ER algorithm), both shown to be specific cases of the AGC rule. Finally, we demonstrate the proposed AGC rule’s practicality and effectiveness using an illustrative example and comparative analysis. The AGC rule has the following advantages of both the analytical algorithm and the generalized combination rule: (1) the fusion result is obtained through a single computational step, (2) weight and reliability are both considered in evidence fusion, and (3) various forms of local ignorance can be handled in the evidence fusion.

In this paper, we prove from a new angle that Dempster's rule is inherently probabilistic, extends Bayes' rule and reduces to Bayes' rule when precise probabilities are available, regardless of whether prior is uniform. We use examples to demonstrate this equivalence. Additionally, we explain that the Evidential Reasoning (ER) rule is also probabilistic and includes Bayes' and Dempster's rules as special cases. Furthermore, we address some criticisms of the behaviour of Dempster's rule from a probabilistic perspective and explain the rationality of the behaviour. We also identify instances where such critiques were misapplied. Finally, we clarify vital differences between belief degrees in belief functions and basic probabilities and highlight the critical differences between Shafer's discounting method and the ER rule. These differences make the latter probabilistic, while the former is not. Our motivation is to show that evidence theory has a probabilistic foundation and is possible to become probabilistic again.

Cross-efficiency evaluation (CEE) is an effective tool for ranking decision-making units (DMUs). The traditional data envelopment analysis (DEA) model employs self-evaluation to measure the performance of DMUs. CEE, as an extension of the DEA, includes self-evaluation and peer-evaluation, assessing the overall performance of each DMU through its own weights and the weights of all DMUs. The current CEE, however, aggregates self-evaluation and peer-evaluation efficiencies mostly via the arithmetic average, which underestimates the importance of self-evaluation and ignores the subjective preferences of decision-makers as well. To address this deficiency, considering the fairness mentality of decision-makers, this paper first introduces the regret theory to depict the regret aversion of decision-makers, and proposes the fair regret cross-efficiency aggregation (FRCEA) method (Method 1). Then the upper and lower limits of the fair regret interval cross-efficiency (FRICE) are calculated, and parameters reflecting the preferences of decision-makers are introduced. Next, this paper puts forth a consensus cross-efficiency aggregation (CCEA) method (Method 2) based on the efficiency expectations of DMUs and the actual aggregation results. By creating a fair evaluation environment, this paper aims to enable all DMUs to participate in the efficiency evaluation and accept the results, reaching a final consensus. Finally, the effectiveness and rationality of the methods above are verified after evaluating the academic research efficiencies of 13 prestigious universities in China.

Graph self-supervised learning is an effective technique for learning common knowledge from unlabeled graph data through pretext tasks. To capture the interrelationships between nodes and their essential roles globally, existing methods use clustering labels as self-supervised signals. However, in some cases, these methods may introduce noise, leading to over-fitting of the model and a reduction in performance. To address these issues, a novel framework for Graph Self-Supervised Curriculum Learning based on clustering label smoothing called GSSCL has been proposed. GSSCL clusters knowledge in an easy-to-difficult manner, reducing the heavy dependence on the reliability of clustering and improving the generalizability of the model. Moreover, the Silhouette Coefficient is employed to evaluate the clustering confident scores for all nodes. Some nodes are selected based on high confident scores to perform self-supervised learning. To account for the possibility of complex heterophilous information in graphs (e.g., noisy links), clustering pseudo-label smoothing is performed on K-nearest neighbor graphs built upon the similarities between node features instead of the original graph structures. The obtained multi-scale knowledge is then applied to curriculum learning. Finally, comprehensive experiments conducted across diverse public graph benchmarks demonstrate the superior performance of the proposed framework. It exhibits comparable results to state-of-the-art methods across semi-supervised node classification and clustering tasks.