In real-world conflicts, decision makers (DMs) often exhibit asymmetric power and distinct behavior patterns, both of which influence DMs’ decision-making processes, thereby affecting the results of conflicts. This paper proposes a data-driven approach to analyze the conflict of DMs’ combinatorial behavior under power asymmetry. Firstly, based on the stability definitions of Graph Model for Conflict Resolution (GMCR) with multi-DMs under power asymmetry, behavioral stability functions for leader and followers are defined. Secondly, the automatic extraction and quantification of the foresight and risk attitudes are realized by the fusion of natural language processing technology, the logic reasoning technology based on production rules and the mathematical statistics method. Therefore the mapping rules of the quantified index to the behavior patterns are given. Finally, the new method is used to analyze the large-scale conflict of “power rationing”. The results show that the proposed method promotes the empirical and operationalization of GMCR, and can provide practical decision-making and diagnostic tools for large-scale conflicts under power asymmetry.

Group conflicts have become increasingly frequent. Owing to information asymmetry among decision makers, unequal resource allocation, and divergent interests, such conflicts often cannot be resolved autonomously. Consequently, the intervention of mediation agencies has become a crucial means for mitigating and resolving disputes. In this study, we develop an option-based conflict resolution optimization model within the Graph Model for Conflict Resolution (GMCR) framework. The model is formulated as a lexicographic bi-objective optimization that first minimizes the number of option adjustments required to satisfy stability requirements and then minimizes the associated adjustment costs. This formulation provides a mathematical foundation for optimizing strategy alignment and achieving more balanced outcomes across conflict groups. To solve the resulting complex nonlinear programming problem, we propose a hybrid solution approach that integrates Genetic Algorithms (GA), Particle Swarm Optimization (PSO), and mathematical programming refinement using Gurobi. In a real-world low-altitude flight-rights allocation case, the proposed approach produces stable mediated outcomes and, relative to baseline methods, achieves fewer adjustments and competitive runtimes while preserving solution quality. The results indicate that the method can serve as a practical and scientifically grounded decision-support tool for group conflict mediation.

Despite substantial exploration of preferences and stabilities in the graph model for conflict resolution (GMCR), there are not enough data to support the existing modeling components. Moreover, multiple dimensional preference structures coexist in complex, real-world, large-scale group (LSG) conflicts. This research addresses these issues with an introduction of big data technology - initiating a big-data-based LSG-GMCR under the three-dimensional preference. This study develops an improved spectral clustering method that combines trusted degrees, sentiments, and similarities to synthesize multi-dimensional attributes, providing a new perspective and a valuable tool for the traditional group conflict analysis. Regarding the clustering algorithm results, a novel big data-based LSG-GMCR under the three-dimensional preference is established to capture and evaluate decision-makers' multi-dimensional preferences and behavioral patterns. Finally, the corresponding matrix representation addresses issues like the model's logic expression complexity and the algorithm generation challenge. The proposed matrix form enhances the model's computational efficiency and the decision support system's realizability. To demonstrate the proposed method performance, it is applied to resolve an electricity rationing conflict in Northeast China and figure out effective resolution strategies.

Failure mode and effects analysis (FMEA), as a well-established risk assessment methodology, has been widely applied across diverse domains. However, current FMEA approaches present certain limitations in representing and fusing uncertain evaluation information, while the integration of team members (TMs)’ social network relationships and consensus-building mechanisms in risk analysis also requires refinement. Therefore, to bridge these research gaps and enhance FMEA reliability, a novel consensus-driven FMEA approach is proposed through the synergistic integration of Dempster-Shafer (D-S) evidence theory with the social network DeGroot (SNDG) model. First, belief structures are employed to precisely model TMs’ complex preferences to address the limitations in representing multiple emotional preferences within evaluation information. Second, a dual-layered network structure combining directed trust relationships and undirected opinion similarity is developed to dynamically determine TMs’ weights for resolving the disconnect between social trust and professional opinions. Third, the maximizing deviation method (MDM) is adopted for objectively determining the weights of risk factor (RFs), while a modified Dempster’s rule (DCR) prevents counterintuitive evidence fusion outcomes. Finally, a novel consensus-reaching process (CRP) incorporating the SNDG model is designed to ensure reliable prioritization of failure modes (FMs) through dynamic opinion adjustment. The effectiveness and superiority of the proposed approach is verified through medical waste management (MWM) case studies, sensitivity analysis, and comparative analysis, with actionable risk rankings being generated to support healthcare risk mitigation strategies. The synergistic integration of D-S evidence theory with dynamic social network consensus mechanisms establishes an innovative framework for risk assessment in complex uncertain environments, combining mathematical rigor with social adaptability.

Subjectivity in classical Graph Model for Conflict Resolution (GMCR) modeling remains a primary concern and scales poorly to large-scale group (LSG) conflicts on social media. In LSG conflicts, (i) difficulties in obtaining and measuring conflict data excessively restrict model objectivity and applications, and (ii) overlapping coalitions create internal vetoes that standard reachability ignores. This motivation calls for a data-driven GMCR that can discover stakeholder groups, quantify overlaps, and preserve interpretability. Accordingly, this research starts from a data perspective and proposes a novel LSG-GMCR model with overlapping coalitions to obtain conflict equilibrium solutions. Considering the requirements of massive data with potential attributes, we employ a crawler algorithm to extract conflict texts from posts, comments, and comment replies on Weibo. A triple conflict data preprocessing mechanism is designed to accurately tackle the scattered forms and large scales. Multiple technologies are integrated to extract features. Then, a meta-clustering algorithm proposed in this paper is constructed for features with different attributes to classify clusters as the group decision makers. A fuzzy membership matrix is also yielded for overlap computation. Finally, the LSG-GMCR model with overlapping is established, supported by the formalized directed overlap and admissibility filter. For validation and verification purposes, this proposed framework is applied to investigate actual conflicts with respect to controversial issues like power rationing conflicts. The approach enhances the scalability, automation, and realism of OR-based conflict analysis and is directly applicable to policy design in complex LSG settings.

With the rise of social media, systematic analysis of consumers’ reviews of new energy vehicles (NEVs) can support market acceptance assessment and inform consumer choice and industry strategy. However, existing studies often rely on single-source data and have difficulty integrating multidimensional information and handling the associated uncertainty. To address this gap, this study proposes a market acceptance evaluation framework based on the directed weighted graph and evidential reasoning (DWG-ER) approach in a cross-dimensional information environment. First, consumer evaluations are collected from two types of cross-dimensional information: individual evaluation information and comparative information. Second, a logistic regression model identifies sentiment in textual reviews from individual evaluations, while a conditional random field model and lexicon-based sentiment analysis extract comparative relations and sentiment orientations from comparative sentences. Third, a novel DWG fusion approach is developed. Comparative sentences are used to determine attribute weights; sentiment analysis results are represented via a dual-layer conversion involving triangular fuzzy numbers and ER belief structures; the ER approach aggregates multi-attribute DWGs; and the resulting ER-based utility values, together with online ratings and voting data, are used to construct a comprehensive DWG. Finally, the PageRank algorithm yields NEV market acceptance rankings, and a case study validates the proposed framework.

Large-scale conflicts characterized by power asymmetry occur frequently in real-world scenarios. However, the current Graph Model for Conflict Resolution (GMCR) is primarily designed for small-scale cases and remains limited by the subjectivity of its modeling inputs. Due to the complexity of conflicts involving numerous decision-makers (DMs), it is essential to develop an objective method to handle large-scale conflicts with power asymmetry. In this paper, we apply objective data and natural language processing (NLP) to create a knowledge graph. This enables the identification of key DMs within clusters, the determination of their pivotal options, and the calculation of their respective weights. This approach addresses the inherent limitations of the traditional GMCR from a data-driven perspective. Furthermore, recognizing that followers are influenced by their leader’s power to varying degrees, a novel GMCR model addressing large-scale asymmetric power conflicts (LS-GMCRPA) is proposed. It measures the willingness of followers to adjust their preferences and introduces new concepts of stability. Additionally, this framework accounts for the interactions among the different DMs’ options under power asymmetry, making it more applicable to real-world scenarios. Finally, we apply this method to a large-scale conflict case, the “Zhengzhou rainstorm”, to demonstrate its effectiveness.

Asymmetric power conflicts arise from resource imbalances among stakeholders, where dominant parties often control situations through rule-setting, while weaker parties face suppression and manipulation. Decision makers (DMs) in such conflicts exhibit bounded rationality and diverse risk attitudes, significantly influencing conflict outcomes. Traditional conflict resolution frameworks, like the graph model for conflict resolution (GMCR), inadequately address power asymmetry and risk attitudes, leading to unrealistic equilibria. This study aims to bridge this gap by integrating risk attitude analysis into the GMCR framework, enhancing its capability to resolve asymmetric power conflicts. Specifically, we introduce a novel approach called triangular fuzzy optimal discrete fitting to assess the risk attitude of DMs amidst asymmetric power conflicts. Additionally, we enhance the principles for categorizing DMs' risk attitude types, surpassing the original optimal discrete fitting method's limitations. Moreover, we define the behavioral pattern stability concepts for the leader and the follower in the GMCR framework during power asymmetry conflicts. Applied to a carbon emission reduction conflict case, we find that as a general risk seeker, although the follower will not choose the options that damage the leader's benefit, it will counter the leader's sanctions by several risky measures for its own benefit. Our methodology and algorithm not only demonstrate practical application but also assist DMs in identifying conflict resolution strategies across varied behavioral patterns.

The rapid growth of the healthcare industry has led to an increase in medical waste, which poses significant public health and environmental challenges worldwide. Therefore, selecting the right location for medical waste disposal plants is crucial. To address this issue, especially when multiple decision-makers are involved, our research developed a social-network group decision-making (SNGDM) framework using incomplete Pythagorean fuzzy preference relations (ICPFPRs). First, targeting the missing information in ICPFPRs, we designed an estimation algorithm to derive complete Pythagorean fuzzy preference relations (CPFPRs). An information uniformity index (IUI) was defined based on the trust scores of experts and the degree of similarity among them within the Pythagorean fuzzy social network. Then, in the consensus-reaching stage, an minimum cost consensus(MCC) model was built to compute CPFPRs with acceptable consistency and group consensus levels. In detail, we introduced a determination method for unit adjustment costs by considering both the confidence level and social influence of experts. Next, the information aggregation and selection were conducted in light of the weights of experts, which were generated by integrating the consistency index, approximation degree, and trust scores. Finally, a numerical example of the site selection of a medical waste disposal plant was presented to validate the presented SNGDM framework. A series of comparison analyses were further carried out to demonstrate the advantages of our proposed method.

Implementing integrated medical-nursing care programs for the elderly is increasingly recognized as a standard approach to address the challenges of elderly care in China. However, fierce conflicts have erupted during the implementation of medical-nursing care due to resource limitations. To achieve viable integration, it is crucial to leverage the government’s inherent power for effectively resolving the current conflicts. Therefore, this paper proposes a negotiation approach aimed at effectively solving the conflicts among the Government, Medical-nursing institutions, and Elderly population in China based on the graph model for conflict resolution under power asymmetry (GMCRPA). The novelty includes demonstrating how medical-nursing institutions and the elderly population can adjust their preferences to reach consensus with the government. Compared with the existing GMCRPA model for two decision-makers (DMs), the complexity of the opponent’s movement patterns is greatly increased in the models including multiple decision-makers. Thus, an approach for calculating the reachable sets of the heterogeneous opponent coalition is presented in this paper. Furthermore, the introduced stability analysis also reflects the interaction of different decision-makers under power asymmetry, which makes the proposal being more in line with real-world scenarios. Finally, the robustness of the proposed method is demonstrated in a practical application aimed at resolving medical-nursing care conflicts. The study offers policymakers conflict negotiation strategies rooted in power theory, facilitating the sustainable implementation of an integrated healthcare system for the aging population.

China is the largest carbon dioxide (CO2) emitter and has formulated CO2 emission peak and carbon-neutral plans. Studies on CO2 emission volume and CO2 emission intensity (CEI) indicate a growing interest in related fields. The purpose of this research is to improve the performance and reliability of the model for forecasting CO2 emissions and judging whether to achieve China's CO2 reduction targets under business-as-usual scenarios. We originally applied a novel hybrid model combining the projection pursuit regression (PPR) model and parasitism-predation optimization algorithm (PPA) (PPA-PPR) to forecast the CO2 emissions from 2022 to 2035, with the time series' CO2 emissions data from 1965 to 2017 and compare with various machine learnings. From the studied results, we can conclude that the hybrid PPA-PPR has better stability and accuracy than BPNN, RF, SVM, GM, TDGM, and LSTM models. The mean absolute percentage error (MAPE) of the verification set data is only 1.19%, and the MAPE of forecasting set data from 2018 to 2021 is 1.44, which obviously outperforms the BPNN, RF, SVM, GM, TDGM, and LSTM models. The second finding is that if China continues to develop in its present trend, it can't implement the CO2 emission peak and reduction CEI target by over 65% by 2030. The limitation of this research is that we don't decompose the time series data into intrinsic modes to study the possibility of improving the model performances.

Asymmetric power conflicts occur frequently. Because of the complexity of the conflict as well as the vagueness of the decision makers’ cognition, it becomes urgent and highly motivated to propose an appropriate method to solve power asymmetry conflict. In this study, we consider that decision makers provide option choices quantified by some degrees of membership. The choice of an option is determined by the thresholds of selection degree. At the same time, due to the influence of the power, the follower adjusts its degree of option choice to reach consensus with the leader. The computational rules determining fuzzy truth value are given, and a fuzzy truth value option prioritization method is proposed to calculate the ranking of the states, where the states ordering is related to the fuzzy degree of option selection. Different from the previous studies, this paper is the first one to study the asymmetric power conflict from the perspective of options, considering the psychological threshold of decision maker for option selection, and pointing out that the option choice is described with the fuzzy values rather than being treated as two-valued (Boolean). Furthermore, the introduced stability analysis also reflects the interaction of the options of different decision makers, which makes the proposal being more in rapport with real-world scenarios. Finally, a case study of carbon emission reduction power asymmetry conflict in supply chain is studied to demonstrate the performance of the proposed method.

Largely inspired by the practice that both the brand name supplier and the platform motivate to encroach on the online retailing market, this paper investigates the optimal encroaching decisions in an online retailing marketplace that is currently owned by multiple online retailers. Depending on whether and who will encroach on, this paper conducts three different encroaching scenarios including the benchmark without encroaching, the brand name supplier encroaching, and the platform encroaching. A Stackelberg game model is then developed to capture competitions among three parties and thus address equilibria in this paper. With analytical studies and numerical experiments, several key findings are derived. For example, but not limited to, the optimal commission set by the platform is contingent largely upon the encroaching scenarios and the number of online retailers. Interestingly, the optimal commission tends to be consistent when there are as many online retailers as possible, regardless of whether and who will encroach. This paper also analytically reveals that the encroaching cost, the product inherent (the fraction of product cost over its market potential), and the optimal commission, induce key impacts on the individuals’ retailing encroaching decisions. A free rider effect incurred by the retailing encroaching is found and examined in this platform supply chain. The results derived in our paper shed lights on operational and encroaching decisions for the platform supply chain.

PurposeThe purpose of the study is to investigate the financing channels and carbon emission abatement preferences of supply chain members, and further examine the optimal contract design of the retailer.Design/methodology/approachThis paper develops a low-carbon supply chain composed of one retailer and one manufacturer, in which the retailer provides trade credit to the manufacturer. Considering the cap-and-trade regulation, the manufacturer with uncertain yield makes decision on whether to invest in emission abatement. There are bank loan and trade credit to finance production for the manufacturer and green credit to finance emission abatement investment. Meanwhile, the retailer may provide the manufacturer with three kinds of contracts to improve emission abatement efficiency, namely, revenue sharing, cost sharing or both sharing.FindingsThe results show that the retailer prefers to offer financing service at lower interest rate, but trade (and green) credit financing is always optimal for manufacturer and supply chain. The investment in emission abatement is value-added to all players. The sharing contracts offered by the retailer at lower sharing ratios can realize Pareto improvement of the system regardless of the financing scheme. However, comparing with the revenue or cost sharing contract, the existence of optimal sharing ratios makes the both sharing contract more favorable to the retailer.Practical implicationsThe findings provide guidance for the emission-dependent manufacturer in financing and emission abatement decisions, as well as recommendations for the retailer to offer loan service and sharing contract.Originality/valueThis paper integrates green credit into bank loan or trade credit to analyze the financing decision of the manufacturer with uncertain yield and further considers the influence of three kinds of sharing contracts introduced by the retailer on improving operational performance.

In social network group decision-making (SNGDM) problems, decision-makers (DMs) often express their opinions or preferences using probabilistic linguistic term sets (PLTSs). In this paper, a novel SNGDM method for probabilistic linguistic information is proposed. Firstly, to obtain the prioritization of DMs in the clustering process, a DM clustering method for SNGDM is developed considering the influence of trust relationships and opinions similarity among DMs. Then, to satisfy the requirements of the consensus reaching process in SNGDM, a dynamic consensus threshold calculation method based on an optimization model is introduced. Furthermore, in the consensus measure stage, a novel consensus measure method for both DMs and subgroups is proposed, using a stochastic multi-criteria acceptability analysis (SMAA) method. Based on the consensus measure method, a novel SNGDM method based on SMAA for PLTSs is proposed. Finally, a case study of service quality evaluation in institutional pensions is used to illustrate the effectiveness of the proposed method. The results of case show that the proposed method can adjust consensus thresholds dynamically based on each round of collective opinions, and can solve the SNGDM problems when DMs can not provide their preferences for criteria weights.

Task allocation is a key aspect of Unmanned Aerial Vehicle (UAV) swarm collaborative operations. With an continuous increase of UAVs’ scale and the complexity and uncertainty of tasks, existing methods have poor performance in computing efficiency, robustness, and real-time allocation, and there is a lack of theoretical analysis on the convergence and optimality of the solution. This paper presents a novel intelligent framework for distributed decision-making based on the evolutionary game theory to address task allocation for a UAV swarm system in uncertain scenarios. A task allocation model is designed with the local utility of an individual and the global utility of the system. Then, the paper analytically derives a potential function in the networked evolutionary potential game and proves that the optimal solution of the task allocation problem is a pure strategy Nash equilibrium of a finite strategy game. Additionally, a PayOff-based Time-Variant Log-linear Learning Algorithm (POTVLLA) is proposed, which includes a novel learning strategy based on payoffs for an individual and a time-dependent Boltzmann parameter. The former aims to reduce the system’s computational burden and enhance the individual’s effectiveness, while the latter can ensure that the POTVLLA converges to the optimal Nash equilibrium with a probability of one. Numerical simulation results show that the approach is optimal, robust, scalable, and fast adaptable to environmental changes, even in some realistic situations where some UAVs or tasks are likely to be lost and increased, further validating the effectiveness and superiority of the proposed framework and algorithm.

The production of fossil energy resources is central to economic development for developing economies such as Ghana, with abundant natural resources, despite the interrelated socio-ecological disruptions. Owing to the value of the newly found oil and gas resources, disputes are sourced from a tradeoff between financial gains and socio-ecological sustainability among multiple decision-makers (DMs) in the Western Region enclave. Strategic negotiations to formally analyze the stability behavior of the government, “fisherfolks,” and oil companies as major DMs with extensive interrelated strategies are necessary for resolving the ongoing conflict. This research proposes a hybrid decision-making trial and evaluation laboratory (DEMATEL) - graph model for conflict resolution (GMCR) method for multiple DMs to analyze complicated conflicts. The DEMATEL method is used to identify critical strategies based on their interrelationship and then analyze the multiple DMs’ stability behavior using an extended matrix-based algorithm within the GMCR model. An algorithm for the proposed hybrid method is put forward and applied to resolve the case of the energy-resource production dispute in Ghana to demonstrate its procedure. The analysis objectively simplifies a complicated conflict and provides strategic insights for policymakers on the stability behavior of multiple DMs that promote sustainable energy resource production.

In the context of “Internet + recycling”, remanufacturing enterprises seek cooperation with recycling platforms to develop online recycling channels. Given that many manufacturers have capital constraints in the recycling and production process, we consider bank and recycling platform to provide financial assistance to the manufacturer. This paper constructs a Stackelberg game model under bank financing and recycling platform financing based on two forms of online recycling cooperation: entrusted recycling and direct recycling. Through the comparison of equilibrium profits, the participants’ financing and recycling channel preferences are explored. The results show that the recycling platform is willing to provide financing service for the manufacturer with a larger capital gap, but there are feasibility conditions for the setting of its loan interest rate. The manufacturer with less initial capital tends to choose the financing scheme with a relatively low interest rate, while the reduction of capital gap increases the propensity for bank financing. The lower platform commission prompts the manufacturer to implement direct recycling, and the increase in cost saving rate of remanufacturing and platform interest rate makes the superiority of direct recycling even more significant. However, entrusted recycling is always more profitable for the recycling platform regardless of the financing scheme. Furthermore, differentiated product sales and portfolio financing can have a certain impact on the manufacturer’s financing and recycling decisions.

China faces a healthcare challenge due to its aging population, necessitating an integrated old-age healthcare system considering multiple stakeholders' interests. Conflict and inequality may arise from varying stakeholder interests. This study develops a conflict resolution strategy for the coordination of stakeholders involved in the old-age healthcare service system, promoting harmonization and minimizing conflict to establish an equitable system meeting elderly needs. It contributes to a robust healthcare system for comprehensive, quality care. The focus of the study is to identify relevant stakeholders and decision-makers involved in developing an integrated old-age healthcare service system and explore a feasible solution through stakeholder analysis using the Mitchell score-based technique and stakeholder theory. Decision-makers' preferences are estimated using the Analytic Hierarchy Process (AHP). Solution strategies are developed through multiple stability concepts within the graph model for conflict resolution (GMCR). The conflict resolution analysis based on the integrated AHP-GMCR approach reveals that the development of an integrated old-age healthcare system is feasible by addressing potential conflicts among the stakeholders. Considering the current predicament of comprehensive medical services in China, governments should distribute authority, simplify procedures, and improve the insurance system. Furthermore, medical institutions should explore funding options, expand services, and enhance accessibility. Elderly individuals should prioritize healthy aging and seek suitable healthcare providers. Stakeholder participation is crucial for effective implementation. These recommendations enable China to advance integrated elderly care successfully, addressing challenges posed by the aging population.

The existing consensus models of conflict decision-making generally assume that the decision-makers’ preferences are simple and certain. This assumption oversimplifies the complexity of real-world conflicts due to the ignorance of the decision-maker’s limited rationality. The present work makes the first attempt at solving this issue by defining the grey consensus and dissent preference of two decision makers (DMs), which is then embedded into the Graph Model for Conflict Resolution (GMCR) to obtain conflict equilibrium solutions. To be specific, preference relations are first described as interval grey scales to reflect the decision maker’s judgments on conflict states, and then converted into crisp values to interface with GMCR. We next present both the logical and matrix representations under the GMCR framework, along with detailed pseudocode that can be implemented to investigate actual conflict situations practically. For validation and verification purposes, the proposed decision framework is applied to the water resource conflict of the Yellow River Basin in China, from which insights are derived to facilitate effective strategic decision-making for resolving complex conflicts in uncertain environments.