Abstract Within the framework of the graph model, a matrix formulation is developed to model and analyze conflicts in which decision makers (DMs) may have reciprocal preferences. Specifically, matrix expressions are employed to represent DMs' reciprocal preference relations, unilateral movements (UMs) and fuzzy unilateral improvements (FUIs), as well as joint UMs and joint FUIs for a coalition of two or more DMs. Furthermore, a matrix methodology is provided to calculate whether a state in a conflict model, or scenario, is stable for a particular DM under various solution concepts, or stability definitions, that reflect the diversity of possible behavioral patterns for a DM in a conflict when preferences can be reciprocal. Five solution concepts associated with reciprocal preferences, Fuzzy Nash Stability, Fuzzy Symmetric Metarationality, Fuzzy General Metarationality, Fuzzy Sequential Stability, and Fuzzy Symmetric Sequential Stability, are redefined for matrix representations of both two-DM and multiple-DM conflict models. To illustrate how the matrix representation can be conveniently employed in practice, it is applied to two real-world conflicts.

中文翻译：

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具有互惠偏好关系的冲突解决图模型稳定性定义的矩阵表示

摘要 在图模型的框架内，开发了一个矩阵公式来建模和分析决策者（DM）可能具有相互偏好的冲突。具体而言，矩阵表达式用于表示 DM 的互惠偏好关系、单边运动 (UM) 和模糊单边改进 (FUI)，以及用于两个或多个 DM 联盟的联合 UM 和联合 FUI。此外，提供了一种矩阵方法来计算冲突模型或场景中的状态对于特定 DM 在各种解决方案概念或稳定性定义下是否稳定，这些解决方案概念或稳定性定义反映了冲突中 DM 的可能行为模式的多样性偏好可以是相互的。与互惠偏好相关的五个解决方案概念，模糊纳什稳定性，模糊对称元理性，模糊一般元理性、模糊顺序稳定性和模糊对称顺序稳定性，被重新定义为双 DM 和多 DM 冲突模型的矩阵表示。为了说明矩阵表示如何在实践中方便地使用，将其应用于两个现实世界的冲突。