Document Type: Research Paper


1 Department of Mathematics, Bankura Christian College, P.O.+ Dist- Bankura, West Bengal,722101, India

2 Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721 102, India


In this paper, we present an application of intuitionistic fuzzy
programming to a two person bi-matrix game (pair of payoffs matrices) for the
solution with mixed strategies using linear membership and non-membership
functions. We also introduce the intuitionistic fuzzy(IF) goal for a choice
of a strategy in a payoff matrix in order to incorporate ambiguity of human
judgements; a player wants to maximize his/her degree of attainment of the IF
goal. It is shown that this solution is the optimal solution of a mathematical
programming problem. Finally, we present a numerical example to illustrate
the methodology.


[1] K. Atanassov, Intuitionistic fuzzy sets: theory and applications, Physica-Verlag, 1999.
[2] P. P. Angelov,Optimization in an intuitinistic fuzzy enviornment, Fuzzy Sets and Systems,
86 (1997), 299-306.
[3] C. R. Bector, S. Chandra and V. Vijay, Bi-matrix games with fuzzy payoffs and fuzzy goals,
Fuzzy Optimization and Decision Making, 3 (2004), 327-344.
[4] T. Basar and G. J. Olsder, Dynamic non-cooperative game theory, Academic Press, New
York, 1995.
[5] L. Campos, Fuzzy linear programming models to solve fuzzy matrix games, Fuzzy Sets and
Systems, 32 (1989), 275-289.
[6] D. Dubois and H. Prade, Fuzzy sets and systems, Academic Press, New York, 1980.
[7] T. Maeda, Characterization of the equilibrium strategy of bi-matrix games with fuzzy payoffs,
Journal of Mathematical Analysis and Applications, 251 (2000), 885-896.
[8] J. V. Neumann and O. Morgenstern, Theory of games and economic behaviour, Princeton
University Press, Princeton, New Jersey, 1944 .
[9] J. F. Nash, Non cooperative games, Annals of Mathematics, 54 (1951), 286-295.
[10] P. K. Nayak and M. Pal, Solution of interval games using graphical method, Tamsui Oxford
Journal of Mathematical Sciences, 22(1) (2006), 95-115.

[11] P. K. Nayak and M. Pal, Bi-matrix games with intuitionistic fuzzy payoffs, Notes on Intuitionistic
Fuzzy Sets, 13(3) (2007), 1-10.
[12] P. K. Nayak and M. Pal, Bi-matrix games with interval payoffs and its Nash equilibrium
strategy, Asia specific Journal of Operational Research, 26(2) (2009), 285-305.
[13] P. K. Nayak and M. Pal, Bi-matrix games with interval payoffs and its Nash equyilibrium
strategy, Journal of Fuzzy Mathematics, 17(2) (2009).
[14] Z. Peng, L. Dagang and W. Guangyuan, Idea and principle of intuitionistic fuzzy optimization,
[15] S. K. Roy, M. P. Biswal and R. N. Tiwari, An approach to multi-objective bimatrix games of
Nash equilibrium solutions, Ricerca Operativa , 30(93) (2001), 47-64.
[16] M. Sakawa and I. Nishizaki, Max-min solution for fuzzy multiobjective matrix games, Fuzzy
Sets and Systems, 67 (1994), 53-69.
[17] M. Sakawa and I. Nishizaki, Equilibrium solution in bi-matrix games with fuzzy payoffs,
Japanse Fuzzy Theory and Systems, 9(3) (1997), 307-324.
[18] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-352.