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

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Fuzzy Information and Engineering

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.

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References

  1. Angelov P P (1997) Optimization in an intuitionistic fuzzy environment. Fuzzy Sets and Systems 86: 299–306

    Article  MathSciNet  MATH  Google Scholar 

  2. Atanassov K T (1986) Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20: 87–96

    Article  MathSciNet  MATH  Google Scholar 

  3. Atanassov K T (1989) More on intuitionistic fuzzy sets. Fuzzy Sets and Systems 33: 37–45

    Article  MathSciNet  MATH  Google Scholar 

  4. Atanassov K T (1994) New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets and Systems 61: 137–142

    Article  MathSciNet  MATH  Google Scholar 

  5. Atanassov K T (1999) Intuitionistic fuzzy sets, Springer-Verlag, Heidelberg

    MATH  Google Scholar 

  6. Bector C R, Chandra S (2002) On duality in linear programming under fuzzy environment. Fuzzy Sets and Systems 125: 317–325

    Article  MathSciNet  MATH  Google Scholar 

  7. Bector C R, Chandra S, Vidyottama V (2004) Matrix games with fuzzy goals and fuzzy linear programming duality. Fuzzy Optimization and Decision Making 3: 255–269

    Article  MathSciNet  MATH  Google Scholar 

  8. Bector C R, Chandra S, Vidyottama V (2004) Duality in linear programming with fuzzy parameters and matrix games with fuzzy payoffs. Fuzzy Sets and Systems 146: 253–269

    Article  MathSciNet  MATH  Google Scholar 

  9. Bector C R, Chandra S (2005) Fuzzy mathematical programming and fuzzy matrix games. Springer-Verlag Berlin

    MATH  Google Scholar 

  10. Bellman R E, Zadeh L A (1970) Decision making in a fuzzy environment. Management Sciences 17: 141–164

    Article  MathSciNet  Google Scholar 

  11. Compos L (1989) Fuzzy linear programming models to solve fuzzy matrix games. Fuzzy Sets and Systems 32: 275–279

    Article  MathSciNet  Google Scholar 

  12. De S K, Biswas R, Roy A R (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets and Systems 117: 209–213

    Article  MathSciNet  MATH  Google Scholar 

  13. Dubois D, Gottwald S, Hajek P, Kacprzyk J, Prade H (2005) Terminological difficulties in fuzzy set theory-the case of intuitionistic fuzzy sets. Fuzzy Sets and Systems 156: 485–491

    Article  MathSciNet  MATH  Google Scholar 

  14. Grzegorzewski P, MrÓwka E (2005) Some notes on (Atanassov’s) multiobjective fuzzy sets. Fuzzy Sets and Systems 156: 492–495

    Article  MathSciNet  MATH  Google Scholar 

  15. Li D F (1999) A fuzzy multiobjective approach to solve fuzzy matrix games. The Journal of Fuzzy Mathematics 7: 907–912

    MATH  Google Scholar 

  16. Li D F (2005) Multiattribute decision making models and methods using intuitionistic fuzzy sets. Journal of Computer and System Sciences 70: 73–85

    Article  MathSciNet  MATH  Google Scholar 

  17. Li D F, Nan J X (2009) A nonlinear programming approach to matrix games with payoffs of Atanassov’s intuitionistic fuzzy sets. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17: 585–607

    Article  MathSciNet  MATH  Google Scholar 

  18. Nan J X, Li D F (2010) A lexicographic method for matrix games with payoffs of triangular intuitionistic fuzzy numbers. International Journal of Computational Intelligence Systems 3(3): 280–289

    Article  Google Scholar 

  19. Nishizaki I, Sakawa M (2001) Fuzzy and multiobjective games for conflict resolution. Springer, Physica-Verleg, Heidelberg

    MATH  Google Scholar 

  20. Szmidt E, Kacprzyk J (1996) Remarks on some application of intuitionistic fuzzy sets in decision making. Notes on IFS 2: 2–31

    MathSciNet  Google Scholar 

  21. Vijay V, Chandra S, Bector C R (2005) Matrix games with fuzzy goals and fuzzy payoffs. Omega 33: 425–429

    Article  Google Scholar 

  22. Vlachos I K, Sergiadis G D (2007) Intuitionistic fuzzy information-applications to pattern recognition. Pattern Recognition Letters 28: 197–206

    Article  Google Scholar 

  23. Yager R (1981) A procedure for ordering fuzzy numbers of the unit interval. Information Sciences 24: 143–161

    Article  MathSciNet  MATH  Google Scholar 

  24. Zimmermann H J (1991) Fuzzy set theory and its applications. Kluwer Academic Publishers, Dordrecht

    MATH  Google Scholar 

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Authors and Affiliations

  1. University School of Basic and Applied Sciences, Guru Gobind Singh Indraprastha University, Delhi, 110403, India

    A. Aggarwal

  2. Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, India

    D. Dubey, S. Chandra & A. Mehra

Authors
  1. A. Aggarwal
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  2. D. Dubey
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  3. S. Chandra
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  4. A. Mehra
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Corresponding authors

Correspondence to A. Aggarwal, D. Dubey, S. Chandra or A. Mehra.

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Aggarwal, A., Dubey, D., Chandra, S. et al. Application of Atanassov’s I-fuzzy set theory to matrix games with fuzzy goals and fuzzy payoffs. Fuzzy Inf. Eng. 4, 401–414 (2012). https://doi.org/10.1007/s12543-012-0123-z

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  • DOI: https://doi.org/10.1007/s12543-012-0123-z

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