求解一类直觉模糊联盟合作博弈Shapley 值的新方法

南江霞,关晶,李登峰

系统科学与数学 ›› 2019, Vol. 39 ›› Issue (4) : 611-621.

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PDF(408 KB)
系统科学与数学 ›› 2019, Vol. 39 ›› Issue (4) : 611-621. DOI: 10.12341/jssms13617
论文

求解一类直觉模糊联盟合作博弈Shapley 值的新方法

    南江霞1,关晶1,李登峰2
作者信息 +

A New Method for Shapley Values of Intuitionistic Fuzzy Coalition Cooperation Games

    NAN Jiangxia1 ,GUAN Jing1 ,LI Dengfeng2
Author information +
文章历史 +

摘要

文章对带有 Choquet 积分的直觉模糊联盟合作博弈 Shapley 值进行了研究. 通过证明一类直觉 模糊联盟合作博弈 Shapley 值满足单调性条件,给出该类直觉模糊联盟合作博弈 Shapley 值的简单计算方法. 该方法是由区间特征函数的上下界直接计算得出直觉模糊联盟合作博弈 Shapley 值的上下界,避免了区间数减法. 此外, 文章又进一步对该类直觉模糊联盟合作博弈 Shapley 值的性质进行了证明. 最后通过数值实例说明该方法的适用性和有效性.

Abstract

In this paper, the Shapley value of intuitionistic fuzzy coalition game with Choquet integrals is studied. By proving that the Shapley value of a class of intuitionistic fuzzy coalition cooperative games satisfies the monotonicity condition, a simple calculation method for the Shapley value of the intuitionistic fuzzy coalition cooperative game is given. In this method, the upper and lower bounds of the Shapley value of the intuitionistic fuzzy coalition cooperative game are directly calculated from the upper and lower bounds of the interval characteristic function, and the method avoids the subtraction of the interval numbers. Furthermore, properties of the Shapley value of the intuitionistic fuzzy coalition game are proved in this paper. Finally, a numerical example is presented to demonstrate the validity and applicability of the method proposed in the paper.

关键词

合作博弈 / 直觉模糊联盟 / 直觉模糊联盟合作博弈 / Shapley 值.

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南江霞 , 关晶 , 李登峰. 求解一类直觉模糊联盟合作博弈Shapley 值的新方法. 系统科学与数学, 2019, 39(4): 611-621. https://doi.org/10.12341/jssms13617
NAN Jiangxia , GUAN Jing , LI Dengfeng. A New Method for Shapley Values of Intuitionistic Fuzzy Coalition Cooperation Games. Journal of Systems Science and Mathematical Sciences, 2019, 39(4): 611-621 https://doi.org/10.12341/jssms13617
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