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高校应用数学学报
高校应用数学学报  2015, Vol. 30 Issue (4): 476-484    
    
残缺模糊合作对策的加权Shapley值
林健1,2, 张强2
1. 福建农林大学 计算机与信息学院, 福建福州 350002
2. 北京理工大学 管理与经济学院, 北京 100081
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
 全文: PDF 
摘要： 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    
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
收稿日期: 2015-01-09 出版日期: 2018-05-19
CLC:  O225  
基金资助: 国家自然科学基金(71371030; 71071018); 高等学校博士学科点专项科研基金(20111101110036); 教育部人文社科研究青年基金(14YJC630114); 福建省教育厅科研基金(JA13114)
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引用本文:

林健, 张强. 残缺模糊合作对策的加权Shapley值[J]. 高校应用数学学报, 2015, 30(4): 476-484.

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.

链接本文:

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

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