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Linear fuzzy game with coalition interaction and its coincident solutions

机译：具有联盟相互作用的线性模糊博弈及其一致解

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摘要

In this study, we consider the solution concepts for fuzzy coalition games (i.e., cooperative games with fuzzy coalition) under a certain participation level. In general, cooperative games with fuzzy coalition are based on the assumption that all the fuzzy coalition values for different fuzzy coalitions must be represented by the same formula, which may omit the coalition interaction under different participation ratios for players. Considering these conditions, we propose the coincident fuzziness form for games with fuzzy coalition, which are represented by a mapping from the characteristic function of the crisp game to that of the fuzzy coalition game. The proposed fuzzy coalition games admit the differences in coalition interactions for different fuzzy coalitions, where the coalition interactions are represented by the fuzzy coalition values in different ways (or formulas). For a fixed fuzzy coalition, the maximum fuzzy coalition game is proven to be the Choquet integral form on the condition that the associate crisp game is convex. In order to seek appropriate solutions for the proposed games based on a certain participation level, the Fuzzy-Shapley axioms are defined, and the explicit Shapley value is represented by the Shapley value of the associated crisp games. Moreover, the fuzzy core of this proposed fuzzy coalition game is the stable solution set for the given fuzzy coalition, which is also denoted by the crisp cores. Furthermore, we study the relationship between the Fuzzy-Shapley value and the fuzzy core. By adding restrictions on the fuzzy core, we propose a strong Fuzzy-core, which is a more stable solution than the fuzzy core. In addition, the fuzzy core is equivalent to the strong Fuzzy-core under some condition. (C) 2018 Elsevier B.V. All rights reserved.
机译：在这项研究中，我们考虑了一定参与水平下的模糊联盟博弈（即具有模糊联盟的合作博弈）的解决方案概念。通常，具有模糊联盟的合作博弈是基于以下假设：不同的模糊联盟的所有模糊联盟值都必须由相同的公式表示，这可能会忽略参与者在不同参与率下的联盟交互。考虑到这些条件，我们提出了模糊联盟博弈的重合模糊形式，其表现形式是从脆性博弈的特征函数到模糊联盟博弈的特征函数的映射。提出的模糊联盟博弈考虑了不同模糊联盟之间联盟交互的差异，其中联盟交互以不同方式（或公式）由模糊联盟值表示。对于一个固定的模糊联盟，在关联明晰博弈是凸的条件下，最大模糊联盟博弈被证明是Choquet积分形式。为了基于一定的参与程度为拟议的游戏寻求适当的解决方案，定义了模糊-萨普利公理，并且明确的Shapley值由关联的清晰游戏的Shapley值表示。此外，该提出的模糊联盟博弈的模糊核心是给定模糊联盟的稳定解集，也用脆核表示。此外，我们研究了Fuzzy-Shapley值和Fuzzycore之间的关系。通过对模糊核增加限制，我们提出了一个强大的模糊核，它是比模糊核更稳定的解决方案。另外，在一定条件下，模糊核等效于强模糊核。 （C）2018 Elsevier B.V.保留所有权利。

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  • 来源
    《Fuzzy sets and systems》 |2018年第15期|1-22|共22页
  • 作者

    Yu Xiaohui; Zhang Qiang; Zhou Zhen;

  • 作者单位

    Beijing Wuzi Univ, Sch Logist, Beijing 101149, Peoples R China;

    Beijing Inst Technol, Sch Management & Econ, Beijing 100081, Peoples R China;

    Capital Normal Univ, Sch Management, Beijing 100089, Peoples R China;

  • 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
  • 中图分类
  • 关键词

    Cooperative game; Core; Fuzzy coalition; Shapley value;

    机译：合作博弈;核心;模糊联盟;沙普利价值;

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