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Core of n-Person Transferable Utility Games with Intuitionistic Fuzzy Expectations

  • Elena Mielcová
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 38)

Abstract

One of the main tasks in the theory of n-person transferable utility games is bound with looking for optimal solution concept. In general, a core is considered to be one of basic used solution concepts. The idea behind core derivation is straightforward; however, in reality uncertainty issues should be taken into consideration. Hence, the main aim of this article is to introduce formalization of the n-person transferable utility games in the case when expected utilities are intuitionistic fuzzy values. Moreover, this article discusses superadditivity issues of intuitionistic fuzzy extensions of cooperative games, and the construction of a core of such games. Calculations are demonstrated on numerical examples and compared with classical game theory results.

Notes

Acknowledgments

This paper was supported by the Ministry of Education, Youth and Sports within the Institutional Support for Long-term Development of a Research Organization in 2015.

References

  1. 1.
    Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Anzilli, L.L., Facchinetti, G., Mastroleo, G.: Evaluation and ranking of intuitionistic fuzzy quantities. In: Masulli, F., Pasi, G., Yager R. (eds.) WILF 2013, LNAI, vol. 8256, pp. 139–149, Springer International Publishing Switzerland (2013)Google Scholar
  3. 3.
    Burillo, P., Bustince, H., Mohedano, V.: Some definitions of intuitionistic fuzzy number. First properties. In: Proceedings of the 1st Workshop on Fuzzy Based Expert Systems, pp. 53–55 (1994)Google Scholar
  4. 4.
    Coker, D.: An Introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets Syst. 88(1), 81, 89 (1997)Google Scholar
  5. 5.
    Grzegorzewski, P.: Distances and orderings in a family of intuitionistic fuzzy numbers. In: Wagenknecht, M., Hampel R. (eds.): Proceedings of EUSFLAT Conference 2003, pp. 223–227 (2003)Google Scholar
  6. 6.
    Li, D.-F.: Decision and game theory in management with intuitionistic fuzzy sets. Studies in fuzziness and Soft computing, vol. 308, Springer, Heidelberg (2014)Google Scholar
  7. 7.
    Mahapatra, G.S., Roy, T.K.: Intuitionistic fuzzy number and its arithmetic operation with application on system failure. J. Uncertain. Syst. 7(2), 92–107 (2013)Google Scholar
  8. 8.
    Mareš, M.: Weak Arithmetics of fuzzy numbers. Fuzzy Sets Syst. 91, 143–153 (1997)CrossRefzbMATHGoogle Scholar
  9. 9.
    Mareš, M.: Additivities in fuzzy coalition games with side-payments. Kybernetika 35(2), 149–166 (1999)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Mareš, M.: Fuzzy Cooperative Games: Cooperation with Vague Expectations. Phisica-Verlag, Heilderberg (2001)CrossRefGoogle Scholar
  11. 11.
    Parvathi, R., Malathi, C.: Arithmetic operations on symmetric trapezoidal intuitionistic fuzzy numbers. Int. J. Soft Comput. Eng. 2(2), 268–273 (2012)Google Scholar
  12. 12.
    Shoham, Y., Leyton-Brown, K.: Multiagent systems: algorithmic, game-theoretic, and logical foundations. Cambridge University Press, Cambridge (2009)Google Scholar
  13. 13.
    Wooldridge, M.J.: An introduction to multiagent systems. Wiley, New York (2002)Google Scholar
  14. 14.
    Xu, Z.S.: Intuitionistic fuzzy aggregation operators. IEEE Trans. Fuzzy Syst. 15, 1179–1187 (2007)CrossRefGoogle Scholar
  15. 15.
    Xu, Z.S., Xia, M.: Induced generalized intuitionistic fuzzy operators. Knowl.-Based Syst. 24, 197–209 (2011)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Informatics and MathematicsSilesian University in Opava, School of Business Administration in KarvinaKarvináCzech Republic

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