A simplified expression of the Shapley function for fuzzy game
A simplified expression of the Shapley function for fuzzy game
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DOI：
10.1016/j.ejor.2008.02.034
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发表时间：
2009-07
期刊：
影响因子：
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通讯作者：
Shujin Li;Qiang Zhang
中科院分区：
文献类型：
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作者：
Shujin Li;Qiang Zhang
本文给出了模糊联盟对策的Shapley函数的一个简化表达式，它可以看作是某些特殊模糊联盟对策中定义的Shapley函数的推广。将Shapley函数的简化表达式与Butnariu，Tsurumi等人建立的两个定义进行了比较，得出了当特征函数为具有比例值的对策时，Shapley函数的简化表达式与Butnariu的定义等价;当特征函数为具有Choquet积分形式的对策时，Shapley函数的简化表达式与Tsurumi的定义等价的结论.从两个参与层次之间相互作用的角度，分别研究了Butnariu和Tsurumi定义的两个博弈的性质。
In this paper, a simplified expression of the Shapley function for games with fuzzy coalition is proposed, which can be regarded as the generalization of Shapley functions defined in some particular games with fuzzy coalition. The simplified expression of the Shapley function is compared with two definitions established by Butnariu, Tsurumi et al. A conclusion is drawn that the simplified expression of the Shapley function is equivalent to Butnariu’s definition when characteristic function is a game with proportional values, and is equivalent to Tsurumi’s definition when characteristic function is a game with Choquet integral forms. Furthermore, from an angle of interaction between two participation levels, the properties of the two games defined by Butnariu and Tsurumi are respectively studied.