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具有区间支付的模糊合作对策上的Shapley函数 被引量：5

The Shapley Function for Fuzzy Cooperative Games with Interval Payoffs
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摘要 利用定义的区间数减法运算法则,探讨了具有区间支付的模糊合作对策.通过对传统模糊合作对策上关于Shapley函数公理体系的推广,给出了具有区间支付的模糊合作对策上Shapley函数的公理特征,并证明了所给区间Shapley函数的存在性和唯一性.最后通过一个算例来说明所给区间Shapley函数的实用性. Fuzzy cooperative games with interval payoffs are discussed by defining subtraction operation for internal numbers. A Shapley function axiomatic system for fuzzy games with interval payoffs is given, which is an extension of the Shapley function axiomatic system for traditional fuzzy games. The existence and uniqueness of the given interval Shapley function are proved. Finally, a numerical example is offered to illustrate the utility of the given interval Shapley function.
作者 孟凡永 张强
机构地区 北京理工大学管理与经济学院
出处 《北京理工大学学报》 EI CAS CSCD 北大核心 2011年第9期1131-1134,共4页 Transactions of Beijing Institute of Technology
基金 国家自然科学基金资助项目(70771010 70801064 71071018)
关键词 区间数 模糊合作对策 Shapley函数 interval numbers fuzzy cooperative games Shapley function
分类号 O225 [理学—运筹学与控制论] O159 [理学—基础数学]
  • 相关文献

参考文献11

  • 1Auhin J P. Mathematical methods of game and economic theory [ M ]. Amsterdam: North-Holland, Dover Publications, 1982.
  • 2Butnariu D. Stability and Shapley value for an n-persons fuzzy game[J]. Fuzzy Sets and Systems, 1980,4(1): 63 - 72.
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二级参考文献5

  • 1陈雯,张强.模糊合作对策的Shapley值[J].管理科学学报,2006,9(5):50-55. 被引量：45
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  • 5Mare S M. Fuzzy coalition structures[J]. Fuzzy Sets and Systems, 2000,114(1) :23 - 33.

共引文献19

同被引文献41

  • 1陈雯,张强.模糊合作对策的Shapley值[J].管理科学学报,2006,9(5):50-55. 被引量：45
  • 2Aubin J ECoeur et valuer des jeux flous a paiement slater- aux[J].Comptes Rendus de I'Aead Sci Paris, 1974,279(6): 891-894.
  • 3Aubin J ECooperative fuzzy games[J].Mathematical Opera- tion Research, 1981,6 ( 1 ) : 1-13.
  • 4Sakawa M, Nishizaki I.A solution concept based on fuzzy decision in n person cooperative games[C]//Proeeedings of Cybernetics and Systems Research.New Jersey,USA:World Scientific Publishing, 1992:423-430.
  • 5Mares M.Coalition forming motivated by vague profits[C]// Proceedings of the Transactions, Mathematical Methods in Economy, Ostrava, 1995 : 114-119.
  • 6Shapley L S.A value for N-person games[J].Annals of Mathe- matical Studies, 1953,28 : 307-317.
  • 7Butnariu D.Stability and Shapley value for an n person fuzzy games[J].Fuzzy Set and System, 1980,4 ( 1 ) : 63-72.
  • 8Tsurumi M, Tanino T, Inuiguchi M.A Shapley function on a class of cooperative fuzzy games[J].European Journal Opera- tional Research, 2001,129 ( 3 ) : 596-618.
  • 9Branzei R, Dimitrov D, Tijs S.Models in cooperative game theory:crisp,fuzzy and multi choice games[M].New York: Springer, 2005.
  • 10Butnariu D, Kroupa T.ShapleY mappings and the cumula- tive value for n person games with fuzzy coalitions[J].Euro- pean Journal of Operational Research, 2008,186( 1 ) : 288-299.

引证文献5

二级引证文献32

北京理工大学学报
2011年 第9期

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