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Application of Atanassov’s I-fuzzy set theory to matrix games with fuzzy goals and fuzzy payoffs

Author

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  • A. Aggarwal

    (Guru Gobind Singh Indraprastha University)

  • D. Dubey

    (Indian Institute of Technology Delhi)

  • S. Chandra

    (Indian Institute of Technology Delhi)

  • A. Mehra

    (Indian Institute of Technology Delhi)

Abstract

We aim to extend some results in [6, 7, 8, 2] on two person zero sum matrix games (TPZSMG) with fuzzy goals and fuzzy payoffs to I-fuzzy scenario. Because the payoffs of the matrix game are fuzzy numbers, the aspiration levels of the players are fuzzy as well. It is reasonable to believe that there is some indeterminacy in estimating the aspiration levels of both players from their respective expected pay offs. This situation is modeled in the game using Atanassov’s I-fuzzy set theory. A new solution concept is proposed for such games and a procedure is outlined to obtain the degrees of suitability of the aspiration levels for each of the two players.

Suggested Citation

  • A. Aggarwal & D. Dubey & S. Chandra & A. Mehra, 2012. "Application of Atanassov’s I-fuzzy set theory to matrix games with fuzzy goals and fuzzy payoffs," Fuzzy Information and Engineering, Springer, vol. 4(4), pages 401-414, December.
    • Handle: RePEc:spr:fuzinf:v:4:y:2012:i:4:d:10.1007_s12543-012-0123-z
    DOI: 10.1007/s12543-012-0123-z
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    References listed on IDEAS

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    1. Vijay, V. & Chandra, S. & Bector, C.R., 2005. "Matrix games with fuzzy goals and fuzzy payoffs," Omega, Elsevier, vol. 33(5), pages 425-429, October.
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    Cited by:

    1. Vishnu Singh & Shiv Prasad Yadav & Sujeet Kumar Singh, 2021. "Duality theory in Atanassov’s intuitionistic fuzzy mathematical programming problems: Optimistic, pessimistic and mixed approaches," Annals of Operations Research, Springer, vol. 296(1), pages 667-706, January.

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