Solution of Matrix Game with Triangular Intuitionistic Fuzzy Pay-Off Using Score Function

Abstract

Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.

Share and Cite:

S. Bandyopadhyay, P. Kumar Nayak and M. Pal, "Solution of Matrix Game with Triangular Intuitionistic Fuzzy Pay-Off Using Score Function," Open Journal of Optimization, Vol. 2 No. 1, 2013, pp. 9-15. doi: 10.4236/ojop.2013.21002.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] I. Nishizaki and M. Sakawa, “Equilibrium Solutions for Multiobjective Bimatrix Games Incorporating Fuzzy Goals,” Journal of Optimization Theory and Applications, Vol. 86, No. 2, 1995, pp. 433-457. doi:10.1007/BF02192089
[2] I. Nishizaki and M. Sakawa, “Max-Min Solution for Fuzzy Multiobjective Matrix Games,” Fuzzy Sets and Systems, Vol. 61, No. 1, 1994, pp. 265-275.
[3] P. K. Nayak and M. Pal, “Solution of Rectangular Fuzzy Games,” OPSEARCH, Vol. 44, No. 3, 2009, pp. 211-226.
[4] P. K. Nayak and M. Pal, “Solution of Interval Games Using Graphical Method,” Tamsui Oxford Journal of Mathematical Sciences, Vol. 22, No. 1, 2006, pp. 95-115.
[5] P. K. Nayak and M. Pal, “Linear Programming Technique to Solve Two Person Matrix Games with Interval Pay- Offs,” Asia-Pacific Journal of Operational Research, Vol. 26, No. 2, 2009, pp. 285-305. doi:10.1142/S0217595909002201
[6] A. L. Narayan, A. R. Meenakshi and A. M. S. Ramasamy, “Fuzzy Games,” The Journal of Fuzzy Mathematics, Vol. 10, 2002, pp. 817-829.
[7] R. E. Moore, “Method and Application of Interval Analysis,” Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1979. doi:10.1137/1.9781611970906
[8] H.-J. Zimmermann, “Fuzzy Mathematical Programming,” Computer Operational Research, Vol. 10, No. 4, 1983, pp. 291-298. doi:10.1016/0305-0548(83)90004-7
[9] K. Atanassov, “Intuitionistic Fuzzy Sets,” Fuzzy Sets and Systems, Vol. 20, No. 1, 1986, pp. 87-96. doi:10.1016/S0165-0114(86)80034-3
[10] K. T. Atanassov, “Ideas for Intuitionistic Fuzzy Equations, Inequalities and Optimization,” Notes on Intuitionistic Fuzzy Sets, Vol. 1, No. 1, 1995, pp. 17-24.
[11] D. F. Li and J. X. Nan, “A Nonlinear Programming Approach to Matrix Games with Payoffs of Atanassov’s Intuitionistic Fuzzy Sets,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 17, No. 4, 2009, pp. 585-607.
[12] M. R. Seikh, M. Pal and P. K. Nayak, “Application of Triangular Intuitionistic Fuzzy Numbers in Bi-Matrix Games,” International Journal of Pure and Applied Ma- thematics, Vol. 79, No. 2, 2012, pp. 235-247.
[13] J.-X. Nan, D.-F. Li and M.-J. Zhang, “A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers,” International Journal of Computational Intelligence Systems, Vol. 3, No. 3, 2010, pp. 280-289. doi:10.2991/ijcis.2010.3.3.4
[14] K. Atanassov, “Intuitionistic Fuzzy Sets: Theory and Applications,” Physica-Verlag, Berlin, 1999. doi:10.1007/978-3-7908-1870-3
[15] M. R. Seikh, M. Pal and P. K. Nayak, “Notes on Triangular Intuitionistic Fuzzy Numbers,” International Journal Mathematics in Operation Research, 2012.
[16] G. S. Mahapatra and T. K. Roy, “Reliability Evaluation Using Triangular Intuitionistic Fuzzy Numbers Arithmetic Operations,” International Journal of Computational and Mathematical Sciences, Vol. 3, No. 5, 2009, pp. 225- 231.
[17] H. B. Mitchell, “Ranking Intuitionistic Fuzzy Numbers,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 12, No. 3, 2004, pp. 377-386. doi:10.1142/S0218488504002886
[18] S.-M. Chen and J.-M. Tan, “Handling Multicriteria Fuzzy Decision Making Problems Based on Vague Set Theory,” Fuzzy Sets and Systems, Vol. 67, No. 2, 1994, pp. 163- 172. doi:10.1016/0165-0114(94)90084-1
[19] D. H. Hong and C.-H. Choi, “Multicriteria Fuzzy Decision Making Problems Based on Vague Set Theory,” Fuzzy Sets and Systems, Vol. 144, No. 1, 2000, pp. 103- 113.
[20] H. W. Liu, “Vague Set Methods of Multicriteria Fuzzy Decision Making,” System Engineering, Theory and Practice, Vol. 5, No. 5, 2004, pp. 214-220.
[21] J. V. Neumann and O. Morgenstern, “Theory of Games and Economic Behaviour,” Princeton University Press, Princeton, 1947.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.