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Fuzzy Multichoice Games with Fuzzy Characteristic Functions

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Abstract

In this paper, a generalized form of fuzzy multichoice games with fuzzy characteristic functions is proposed, which can be seen as an extension of traditional fuzzy games. Based on the extension Hukuhara difference, fuzzy multichoice games with fuzzy characteristic functions are studied, and a Shapley function is discussed. The notion of fuzzy multichoice population monotonic allocation scheme (FMPMAS) is defined. When the given fuzzy multichoice game with fuzzy characteristic functions is convex, we show that the proposed Shapley function is a FMPMAS. Furthermore, two special kinds of fuzzy multichoice games with fuzzy characteristic functions called fuzzy multichoice games with multilinear extension form and fuzzy characteristic functions and fuzzy multichoice games with Choquet integral form and fuzzy characteristic functions are researched.

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References

  • Aubin JP (1974) Coeur et valeur des jeux flous à paiements latéraux. C R Hebdomad D 279-A:891–894

    Google Scholar 

  • Banks HT, Jacobs MQ (1970) A differential calculus for multifunctions. J Math Anal Appl 29:246–272

    Article  Google Scholar 

  • Borkotokey S (2008) Cooperative games with fuzzy coalitions and fuzzy characteristic functions. Fuzzy Sets Syst 159:138–151

    Article  Google Scholar 

  • Butnariu D (1980) Stability and Shapley value for an \(n\)-persons fuzzy game. Fuzzy Sets Syst 4:63–72

    Article  Google Scholar 

  • Butnariu D, Kroupa T (2008) Shapley mappings and the cumulative value for \(n\)-person game with fuzzy coalitions. Eur J Oper Res 186:288–299

    Article  Google Scholar 

  • Calvo E, Santos JC (2000) A value for multichoice games. Math Soc Sci 40:341–354

    Article  Google Scholar 

  • Derks J, Peters H (1993) A Shapley value for games with restricted coalitions. Int J Game Theory 21:351–360

    Article  Google Scholar 

  • Dubois D, Kerre E, Mesiar R, Prade H (2000) Fuzzy interval analysis. Kluwer, Dordrecht

    Book  Google Scholar 

  • Hsiao CR, Raghavan TES (1993) Shapley value for multi-choice cooperative games(I). Game Theory Econ Behav 5:240–256

    Article  Google Scholar 

  • Hwang YA, Liao YH (2008) Potential in multi-choice cooperative TU games. Asia Pac J Oper Res 25:591–611

    Article  Google Scholar 

  • Hwang YA, Liao YH (2009) Equivalence theorem, consistency and axiomatizations of a multi-choice value. J Glob Optim 45:597–613

    Article  Google Scholar 

  • Klijn F, Slikke M, Zarzuelo J (1999) Characterizations of a multi-choice value. Int J Game Theory 28:521–532

    Article  Google Scholar 

  • Li SJ, Zhang Q (2009) A simplified expression of the Shapley function for fuzzy game. Eur J Oper Res 196:234–245

    Article  Google Scholar 

  • Mares M (2000) Fuzzy coalition structures. Fuzzy Sets Syst 114:23–33

    Article  Google Scholar 

  • Mares M, Vlach M (2001) Linear coalition games and their fuzzy extensions. Int J Uncertain Fuzziness 9:341–354

    Article  Google Scholar 

  • Meng FY, Zhang Q (2010) The Shapley function for fuzzy cooperative games with multilinear extension form. Appl Math Lett 23:644–650

    Article  Google Scholar 

  • Meng FY, Zhang Q (2014) A coalitional value for multichoice games with a coalition structure. Appl Math Inf Sci 8:193–203

    Article  Google Scholar 

  • Meng FY, Tan CQ, Zhang Q (2014) The generalized symmetric coalitional Banzhaf value for multichoice games with a coalition structure. J Syst Sci Complex 27:1064–1078

    Article  Google Scholar 

  • Peters H, Zank H (2005) The egalitarian solution for multichoice games. Ann Oper Res 137:399–409

    Article  Google Scholar 

  • Sakawa M, Nishizaki I (1994) A lexicographical solution concept in an \(n\)-person cooperative fuzzy game. Fuzzy Sets Syst 61:265–275

    Article  Google Scholar 

  • Shapley LS (1953) A value for \(n\)-persons games. Ann Math Stud 28:307–318

    Google Scholar 

  • Shapley LS (1971) Cores of convex games. Int J Game Theory 1:11–26

    Article  Google Scholar 

  • Sprumont Y (1990) Population monotonic allocation schemes for cooperative games with transferable utility. Games Econ Behav 2:378–394

    Article  Google Scholar 

  • Tijs S, Branzei R, Ishihara S, Muto S (2004) On cores and stable sets for fuzzy games. Fuzzy Sets Syst 146:285–296

    Article  Google Scholar 

  • Tsurumi M, Tanino T, Inuiguchi M (2001) A Shapley function on a class of cooperative fuzzy games. Eur J Oper Res 129:596–618

    Article  Google Scholar 

  • van den Nouweland A, Tijs Potters J, Zarzuelo J (1995) Cores and related solution concepts for multi-choice games. Math Methods Oper Res 41:289–311

    Article  Google Scholar 

  • Yu XH, Zhang Q (2009) The fuzzy core in games with fuzzy coalitions. J Comput Appl Math 230:173–186

    Article  Google Scholar 

  • Yu XH, Zhang Q (2010) An extension of cooperative fuzzy games. Fuzzy Sets Syst 161:1614–1634

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  Google Scholar 

  • Zadeh LA (1973) The concept of a linguistic variable and its application to approximate reasoning. American Elsevier Publishing Company, New York

Download references

Acknowledgments

The authors first gratefully thank the Editor-in-Chief, the Associate Editor and the anonymous referee for their valuable and constructive comments which have much improved the paper. This work was supported by the State Key Program of National Natural Science of China (No. 71431006), the National Natural Science Foundation of China (Nos. 71571192, 71501189, 71271217, 71401003), the China Postdoctoral Science special Foundation (2015T80901), the China Postdoctoral Science Foundation (2014M560655), the Innovation-Driven Planning Foundation of Central South University (2015CX010), and the Program for New Century Excellent Talents in University of China (No. NCET-12-0541).

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Authors and Affiliations

  1. School of International Audit, Nanjing Audit University, No. 86 Yushan Road, Jiangpu street, Nanjing, 211815, Pukou District, China

    Fanyong Meng

  2. Business School, Central South University, No. 932 South Lushan Road, Changsha, 410083, Hunan, People’s Republic of China

    Fanyong Meng & Xiaohong Chen

  3. School of Management and Economics, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, Beijing, 100081, People’s Republic of China

    Qiang Zhang

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  1. Fanyong Meng
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  2. Qiang Zhang
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  3. Xiaohong Chen
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Correspondence to Fanyong Meng.

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Meng, F., Zhang, Q. & Chen, X. Fuzzy Multichoice Games with Fuzzy Characteristic Functions. Group Decis Negot 26, 565–595 (2017). https://doi.org/10.1007/s10726-016-9493-7

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