Max-min solution approach for multi-objective matrix game with fuzzy goals
DOI:
https://doi.org/10.2298/YJOR140415008KKeywords:
multi-objective matrix game, fuzzy goal, max-min solutionAbstract
In this paper, we consider a multi-objective two person zero-sum matrix game with fuzzy goals, assuming that each player has a fuzzy goal for each of the payoffs. The max-min solution is formulated for this multi-objective game model, in which the optimization problem for each player is a linear programming problem. Every developed model for each player is demonstrated through a numerical example.References
Bandyopadhyay, S. and Nayak, P.K., “Matrix games with trapezoidal fuzzy pay offs”, International Journal of Engineering Research and Development, 5 (2013) 21-29.
Bandyopadhyay, S., Nayak, P.K. and Pal, M., “Solution of matrix game with triangular intuitionistic fuzzy pay-off using score function”, Open Journal of Optimization, 2 (2013) 9-15.
Bector, C.R. and Chandra, S., “On duality in linear programming under fuzzy environment”, Fuzzy Sets and Systems, 125 (2002) 317-325.
Bector, C.R. and Chandra, S., Fuzzy Mathematical Programming and Fuzzy Matrix Games, Springer, Berlin, Heidelberg, 2004.
Bector, C.R., Chandra, S. and Vijay, V., “Duality in linear programming with fuzzy parameters and matrix games with fuzzy payoffs”, Fuzzy Sets and Systems, 146 (2004) 253-269.
Bector, C.R., Chandra, S. and Vijay, V., “Matrix games with fuzzy goals and fuzzy linear programming duality”, Fuzzy Optimization and Decision Making, 3 (2004) 255-269.
Bellman, R.E. and Zadeh, L.A., “Decision-making in a fuzzy environment”, Management Science, 17 (4) (1970) 141-164.
Campos, L., “Fuzzy linear programming models to solve fuzzy matrix games”, Fuzzy Sets and Systems, 32 (1989) 275-289.
Çevikel, A.C. and Ahlatçıoglu, M., “A linear interactive solution concept for fuzzy multiobjective games”, European Journal of Pure and Applied Mathematics, 35 (2010) 107-117.
Chen, Y.W. and Larbani, M., “Two-person zero-sum game approach for fuzzy multiple attribute decision making problems”, Fuzzy Sets and Systems, 157 (2006) 34-51.
Gupta, P. and Mehlawat, M.K., “Bector-Chandra type duality in fuzzy linear programming with exponential membership functions”, Fuzzy Sets and Systems, 160 (2009) 3290-3308.
Li, D.F. and Hong, F.X., “Solving constrained matrix games with payoffs of triangular fuzzy numbers”, Computers & Mathematics with Applications, 64 (2012) 432-448.
Lin, R., “Note on fuzzy sets”, Yugoslav Journal of Operations Research, 23 (2013) 1-5.
Nan, J.X., Li, D.F. and Zhang, M.J., “A lexicographic method for matrix games with payoffs of triangular intuitionistic fuzzy numbers”, International Journal of Computational Intelligence Systems, 3 (2010) 280-289.
Pandey, D. and Kumar, S., “Modified approach to multiobjective matrix game with vague payoffs”, Journal of International Academy of Physical Sciences, 14 (2) (2010) 149-157.
Pandey, D. and Kumar, S., “Fuzzy Optimization of Primal-Dual Pair Using Piecewise Linear Membership Functions”, Yugoslav Journal of Operations Research, 22 (2) (2012) 97-106.
Sakawa, M. and Nishizaki, I., “Max-min solutions for fuzzy multiobjective matrix games”, Fuzzy Sets and Systems, 67 (1994) 53-69.
Vijay, V., Chandra, S. and Bector, C.R., “Matrix games with fuzzy goals and fuzzy payoffs”, Omega, 33 (2005) 425-429.
Vijay, V., Mehra, A., Chandra, S. and Bector, C.R., “Fuzzy matrix games via a fuzzy relation approach”, Fuzzy Optimization and Decision Making, 6 (2007) 299-314.
Zhou, X., Song, Y., Zhang, Q. and Gao, X., “Multiobjective matrix game with vague payoffs”, ICFIE, ASC 40, 543-550.
Downloads
Published
Issue
Section
License
Copyright (c) 2016 YUJOR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
