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Bimatrix Games with Intuitionistic Fuzzy Payoffs

  • Tina VermaEmail author
  • Amit Kumar
Chapter
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 383)

Abstract

Li and Yang [2] pointed out that there is no method in the literature for solving such bimatrix games or two person non-zero sum games (matrix games in which gain of one player is not equal to the loss of other player) in which payoffs are represented by intuitionistic fuzzy numbers and proposed a method for the same. In this chapter, it is pointed out that Li and Yang have considered some mathematically incorrect assumptions in their proposed method. For resolving the shortcomings of Li and Yang’s method, a new method (named as Mehar method) is proposed. Also, the exact optimal solution of the numerical problem, solved by Li and Yang by their pro-posed method, is obtained by the proposed Mehar method.

References

  1. 1.
    Li, D.F.: A ratio ranking method for triangular intuitionistic fuzzy numbers and its application to MADM problems. Comput. Math. Appl. 60, 1557–1570 (2010)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Li, D.F., Yang, J.: A difference-index based rank-ing bilinear programming approach to solving bimatrix games with payoffs of trapezoidal intuitionistic fuzzy numbers. J. Appl. Math. 2013, 1–10 (2013)Google Scholar
  3. 3.
    Mangasarian, O.L., Stone, H.: Two-person nonzero-sum games and quadratic programming. J. Math. Anal. Appl. 9, 348–355 (1964)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology RoparRupnagarIndia
  2. 2.School of MathematicsThapar Institute of Engineering and TechnologyPatialaIndia

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