Matrix representation of stability definitions for the graph model for conflict resolution with reciprocal preference relations

Wu Nannan; Kilgour D. Marc; Hipel Keith W.; Xu Yejun

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Matrix representation of stability definitions for the graph model for conflict resolution with reciprocal preference relations

机译：与互惠偏好关系相互偏好关系图形模型的稳定性定义的矩阵表示

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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. (C) 2020 Elsevier B.V. All rights reserved.

机译：在图形模型的框架内，开发了矩阵制剂以模拟和分析决策者（DMS）可能具有互惠偏好的冲突。具体地，采用矩阵表达来代表DMS互惠偏好关系，单边运动（UMS）和模糊单方面改进（FUIS），以及两个或多个DMS联盟的联合UMS和联合FUI。此外，提供了一种矩阵方法来计算冲突模型中的状态，或场景，在各种解决方案概念或稳定性定义下对特定DM稳定，其反映冲突时可能在冲突中的可能行为模式的多样性偏好可以是互惠的。五个与互惠偏好相关的解决方案概念，模糊纳什稳定性，模糊对称性等性，模糊通用性等性，模糊顺序稳定性和模糊对称顺序稳定性，用于重新定义两-DM和多DM冲突模型的矩阵表示。为了说明如何在实践中方便地使用矩阵表示，它应用于两个真实的冲突。（c）2020 Elsevier B.v.保留所有权利。

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来源
《Fuzzy sets and systems》 |2021年第15期|32-54|共23页
作者
Wu Nannan; Kilgour D. Marc; Hipel Keith W.; Xu Yejun;
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作者单位

Hohai Univ Business Sch Res Inst Management Sci Nanjing 211100 Peoples R China|Univ Waterloo Dept Syst Design Engn Waterloo ON N2L 3G1 Canada;

Univ Waterloo Dept Syst Design Engn Waterloo ON N2L 3G1 Canada|Wilfrid Laurier Univ Dept Math Waterloo ON N2L 3C5 Canada;

Univ Waterloo Dept Syst Design Engn Waterloo ON N2L 3G1 Canada|Ctr Int Governance Innovat Waterloo ON N2L 6C2 Canada|Balsillie Sch Int Affairs Waterloo ON N2L 6C2 Canada;

Hohai Univ Business Sch Res Inst Management Sci Nanjing 211100 Peoples R China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
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关键词
Reciprocal preferences; Graph model for conflict resolution; Matrix representation; Stability definitions;

机译：互惠偏好;冲突分辨率的图模型;矩阵表示;稳定性定义;

Matrix representation of stability definitions for the graph model for conflict resolution with reciprocal preference relations

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