Linear programming models to solve fully fuzzy two person zero sum matrix game
Downloads
DOI:
https://doi.org/10.26637/MJM0803/0007Abstract
This paper presents a new method for solving the two person zero sum matrix game with fuzzy payoffs and fuzzy strategies for the players. Ranking function of triangular fuzzy numbers is used to develop a pair of crisp linear programming models corresponding to each player. Every established model for each player is illustrated through a numerical example. Sensitivity analysis with respect to different parameters on value of game and strategies of players are demonstrated by graphs.
Keywords:
Two person zero sum matrix game, fuzzy number, fuzzy ranking, defuzzificationMathematics Subject Classification:
Mathematics- Pages: 775-781
- Date Published: 01-07-2020
- Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)
J. M. Adamo, Fuzzy decision trees, Fuzzy Sets Syst., 4(1980), 207-219.
A. Aggarwal, D. Dubey, S. Chandra and A. Mehra, Application of Atanassov's I-fuzzy set theory to matrix games with fuzzy goals and fuzzy payoffs, Fuzzy Inf. Eng., 4(2012), 401-414.
A. Aggarwal, A. Mehra and S. Chandra, Application of linear programming with I-fuzzy sets to matrix games with I-fuzzy goals, Fuzzy Optim. Decis. Ma., 11(4)(2012), $465-480$.
K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., $20(1)(1986), 87-96$.
K. T. Atanassov, Intuitionistic fuzzy sets: theory and applications, Physica-Verlag, Heidelberg, 1999.
C. R. Bector, S. Chandra and V. Vijay, Duality in linear programming with fuzzy parameters and matrix games with fuzzy payoffs, Fuzzy Sets Syst., 146(2004), 253-269.
L. Campos, Fuzzy linear programming models to solve fuzzy matrix games, Fuzzy Sets Syst., 32(3)(1989), 275 289.
L. Campos, A. Gonzalez and M. A. Vila, On the use of the ranking function approach to solve fuzzy matrix games in a direct way, Fuzzy Sets Syst., 49(1992), 193-203.
A. C. Cevikel and M. Ahlatcioglu, Solutions for fuzzy matrix games, Comput. Math. Appl., 60(2010), 399-410.
S. H. Chen and C. H. Hsieh, Graded mean integration representation of generalized fuzzy numbers, Journal of Chinese Fuzzy Systems Association, 5(2)(1999), 1-7.
Y. W. Chen and M. Larbani, Two person zero sum game approach for fuzzy multiple attribute decision making problems, Fuzzy Sets Syst., 157(2006), 34-51.
M. S. Garcia and M. L. Lamata, A modification of the index of Liou and Wang for ranking fuzzy numbers, Int. J. Uncertain. Fuzz., 15(4)(2007), 411-424.
J. Jana and S. K. Roy, Solution of matrix games with generalized trapezoidal fuzzy payoffs, Fuzzy Inf. Eng., 10(2)(2018), 213-224.
G. Krishnaveni and K. Ganesan, New approach for the solution of two person zero sum fuzzy games, Int. J. Pure Appl. Math., 119(9)(2018), 405-414.
R. S. Kumar and D. Keerthana, A solution of fuzzy game matrix using defuzzification method, Malaya Journal of Matematik, 5(1)(2015), 68-72.
D. F. Li, A fuzzy multi-objective approach to solve fuzzy matrix games, J. Fuzzy Math., 7(1999), 907-912.
D. F. Li and C. T. Cheng, Fuzzy multi-objective programming methods for fuzzy constrained matrix games with fuzzy numbers, Int. J. Uncertain. Fuzz., 10(4)(2002).
$[18]$ T. S. Liou and M. J. Wang, Ranking fuzzy numbers with integral value, Fuzzy Sets Syst., 50(3)(1992), 247-255.
T. Maeda, On characterization of equilibrium strategy of two person zero sum games with fuzzy payoffs, Fuzzy Sets Syst., 139(2003), 283-296.
J. X. Nan and D. F. Li, Linear programming approach to matrix games with intuitionistic fuzzy goals, Int. J. Comput. Int. Sys., 6(1)(2013), 186-197.
J. V. Neumann and O. Morgenstern, Theory of games and economic behavior, Princeton University Press, 1944.
I. Nishizaki and M. Sakawa, Fuzzy and multi-objective games for conflict resolution, Physica-Verlag, Heidelberg, 2001.
S. K. Roy and S. N. Mondal, An approach to solve fuzzy interval valued matrix games, Int. J. Oper. Res., 26(3)(2016), 253-267.
S. K. Roy and P. Mula, Solving matrix game with rough payoffs using genetic algorithm, Int. J. Oper. Res., 16(1)(2016), 117-130.
M. Sakawa and I. Nishizaki, Max-min solutions for fuzzy multi-objective matrix games, Fuzzy Sets Syst., 67(1)(1994), 53-69.
M. R. Seikh, P. K. Nayak and M. Pal, Matrix games with intuitionistic fuzzy payoffs, Journal of Information and Optimization Sciences, 36(1-2)(2015), 159-181.
S. C. Sharma and G. Kumar, A computational approach to solve games with uncertainty and an application in election forecasting, Jananabha, 46(2016), 75-86.
B. K. Tripathy, S. P. Jena and S. K. Ghosh, An intuitionistic fuzzy count and cardinality of intuitionistic fuzzy sets, Malaya Journal of Matematik, 4(1)(2013), 123-133.
V. Vijay, S. Chandra and C. R. Bector, Matrix games with fuzzy goals and fuzzy payoffs, Omega, 33(2005), $425-429$.
R. R. Yager, A procedure for ordering fuzzy numbers of the unit interval, Inf. Sci., 24(1981), 143-161.
L. A. Zadeh, Fuzzy sets, Inform. Contr., 8(1965), 338353.
- NA
Similar Articles
- Sankar Das, Similarity measures on intuitionistic fuzzy matrices and its applications , Malaya Journal of Matematik: Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.
