Most existing work on three-way conflict analysis has focused on trisecting agent pairs, agents, or issues, which contributes to understanding the nature of conflicts but falls short in addressing their resolution. Specifically, the formulation of feasible strategies, as an essential component of conflict resolution and mitigation, has received insufficient scholarly attention. Therefore, this paper aims to investigate feasible strategies from two perspectives of consistency and non-consistency. Particularly, we begin with computing the overall rating of a clique of agents based on positive and negative similarity degrees. Afterwards, considering the weights of both agents and issues, we propose weighted consistency and non-consistency measures, which are respectively used to identify the feasible strategies for a clique of agents. Algorithms are developed to identify feasible strategies, $L$-order feasible strategies, and the corresponding optimal ones. Finally, to demonstrate the practicality, effectiveness, and superiority of the proposed models, we apply them to two commonly used case studies on NBA labor negotiations and development plans for Gansu Province and conduct a sensitivity analysis on parameters and a comparative analysis with existing state-of-the-art conflict analysis approaches. The comparison results demonstrate that our conflict resolution models outperform the conventional approaches by unifying weighted agent-issue evaluation with consistency and non-consistency measures to enable the systematic identification of not only feasible strategies but also optimal solutions.
With societal progress, conflicts have become more widespread and intricate across various levels of individual, group, and organizational, where agents often exhibit opposing attitudes or behaviors due to differences in goals, resources, interests, and other factors. Conflict analysis has emerged as a critical field, offering a robust framework for understanding and resolving conflicts [1][2][3][4][5][6][7][8][9][10]. Early works by Pawlak [1,2] introduced the concept of evaluating relationships between two agents as alliance, neutrality, or conflict using auxiliary functions, laying the foundation for conflict analysis using rough set theory. Deja [5] expanded on Pawlak's model by integrating Boolean reasoning, thereby offering a deeper understanding of conflict and addressing three core questions related to conflict resolution.
The theory of three-way decision [11][12][13][14] is closely aligned with human cognitive processes, facilitating thinking, problem-solving, and information processing by conceptualizing decisions in terms of three elements. The Triading-Acting-Optimizing model [14] presents a framework for three-way decision, which involves a Triading step for forming a triad of three elements, an Acting step for applying distinct strategies to process these elements, and an Optimizing step to evaluate and refine the overall outcome. In a more focused sense, the philosophy and methodology of three-way decision have been applied to various specific topics [15][16][17][18][19][20][21][22][23][24][25]. Three-way conflict analysis, as one of these topics, seeks to reinforce the application of three-way decision and conflict analysis, supported by their shared foundations in decision-making and strategy formulation. Furthermore, various models of conflict analysis have also been investigated, including formal concept-based conflict analysis [26,27], reduction-combined conflict analysis [28,29], conflict analysis with agent-agent mutual selection [30], preference-based conflict analysis [31], and multi-scale and multi-source conflict analysis [32,33]. Current literature has explored three-way conflict analysis from two main perspectives: trisections regarding agents and issues [34][35][36][37][38][39][40], corresponding to the Triading step, and feasible strategies [41][42][43][44][45][46][47][48][49], corresponding to the Acting step.
The literature highlights several important trisections in conflict analysis. The first is the trisection of agent pairs, representing three types of agent relations. Lang, Miao, and Cai [34] integrated three-way decision theory and decision-theoretic rough sets into conflict analysis, defining probabilistic conflict, neutrality, and alliance relations, which form a trisection of agent pairs. They used decision-theoretic rough sets to compute thresholds for the trisection. Yao [35] introduced a distance function to analyze the trisection of agent pairs, categorizing conflicts into strong-, weak-, and non-conflict levels. Xu and Jia [36] applied similarity functions to analyze the trisection of agent pairs in the context of single and multiple issues and proposed a method for selecting optimal trisection thresholds based on a measure. The second is the trisection of individual agents, representing their alliances or groups. Lang, Miao, and Fujita [37] explored three-way group conflict using Pythagorean fuzzy information, defining positive, neutral, and negative alliances based on fuzzy loss functions and Bayesian minimal risk theory. Li et al. [38] applied triangular fuzzy situation tables to evaluate agent attitudes toward multiple issues, using decisiontheoretic rough sets to calculate two thresholds for the trisection. In a subsequent study [39], they extended this analysis to multiple issues with trapezoidal fuzzy situation tables. The third is the trisection of individual issues.
Zhi et al. [40] proposed a novel conflict analysis framework based on three-way concept analysis, particularly for conflict situations involving one-vote veto. They identified the maximum alliance and minimum conflict sets within cliques based on the allied, conflict, and neutral issues. While these studies successfully employ trisections to uncover the fundamental nature of conflicts, the formulation of practical solutions remains the ultimate objective.
Therefore, the immediate priority is to explore feasible strategies for effectively resolving conflict problems.
To construct feasible strategies, Sun, Ma, and Zhao [41] introduced a matrix-based approach grounded in rough sets over two universes to identify the root causes of conflict and derive the maximum feasible consensus strategies in conflict situations. They later extended their model into a probabilistic context [42]. Xu et al. [44] developed consistency measures to assess the similarity between agents’ attitudes and consensus attitudes, defining L-order dominant feasible strategies based on the consistency degree of a clique
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