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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2015, Vol. 30 Issue (4): 476-484    DOI:
    
Weighted Shapley value for cooperative games with fuzzy coalition and incomplete information
LIN Jian1,2, ZHANG Qiang2
1. College of Computer and Information, Fujian Agriculture and Forestry University, Fuzhou 350002, China
2. School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China
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Abstract  With respect to cooperative game with fuzzy coalitions, in which the payoffs information are partially known, the definition of $E$-incompelte fuzzy games is introduced. The $w$-weighted Shapley value, which satisfies linearity and symmetry, is proposed based on the cardinality set of incomplete coalition value. By considering the marginal contribution between coalitions, the equivalent form of $w$-weighted Shapley value is provided. The study showes that the Shapley value for complete fuzzy cooperative games in accordance with the $w$-weighted Shapley value. In the frame of fuzzy coalitions, some desirable properties of $w$-weighted Shapley value, such as coalition monotonicity, zero-normalization, etc, are discussed in detail. Finally, a numerical example is illustrated to show the validity of the $w$-weighted Shapley value.

Key words： cooperative game      fuzzy coalition      incomplete information      Shapley value     
Received: 09 January 2015      Published: 19 May 2018
CLC:  O225  
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Cite this article:

LIN Jian, ZHANG Qiang. Weighted Shapley value for cooperative games with fuzzy coalition and incomplete information. Applied Mathematics A Journal of Chinese Universities, 2015, 30(4): 476-484.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2015/V30/I4/476


残缺模糊合作对策的加权Shapley值

针对具有模糊联盟且支付值残缺的合作对策问题, 给出了$E$-残缺模糊对策的定义. 基于残缺联盟值基数集, 提出了一个同时满足对称性和线性性的$w$-加权Shapley值公式. 通过构造模糊联盟间的边际贡献, 探讨了$w$-加权Shapley值公式的等价表示形式, 指出$w$-加权Shapley值与完整合作对策Shapley 值的兼容性. 在模糊联盟框架里, 探讨了$w$-加权Shapley 值所满足的联盟单调性、零正则性等优良性质. 最后通过算例验证了该公式的有效性.

关键词： 合作对策,  模糊联盟,  信息残缺,  Shapley值 
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