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Solving multi-objective fuzzy matrix games via multi-objective linear programming approach
Kybernetika, Tome 52 (2016) no. 1, pp. 153-168 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A class of multi-objective fuzzy matrix games is studied and it is shown that solving such a game is equivalent to solving a pair of multi-objective linear programming problems. This work generalizes an earlier study of Fernandez et al. [7] from crisp scenario to fuzzy scenario on the lines of Bector et al. [4]. Further certain difficulties with similar studies reported in the literature are also discussed.
A class of multi-objective fuzzy matrix games is studied and it is shown that solving such a game is equivalent to solving a pair of multi-objective linear programming problems. This work generalizes an earlier study of Fernandez et al. [7] from crisp scenario to fuzzy scenario on the lines of Bector et al. [4]. Further certain difficulties with similar studies reported in the literature are also discussed.
DOI : 10.14736/kyb-2016-1-0153
Classification : 90C70, 91A40
Keywords: multi-objective game; Pareto-optimal security strategies; security level; multi-objective linear programming 
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Aggarwal, Abha; Khan, Imran. Solving multi-objective fuzzy matrix games via multi-objective linear programming approach. Kybernetika, Tome 52 (2016) no. 1, pp. 153-168. doi: 10.14736/kyb-2016-1-0153

[1] Bellman, R. E., Zadeh, L. A.: Decision making in a fuzzy environment. Management Sci. 17 (1970), 141-164. | DOI | MR | Zbl

[2] Blackwell, D.: An analog of the minimax theorem for vector payoff. Pacific J. Math. 6 (1956), 1-8. | DOI | MR

[3] Bector, C. R., Chandra, S., Vijay, V.: Matrix games with fuzzy goals and fuzzy linear programming duality. Fuzzy Optim. Decision Making 3 (2004), 263-277. | DOI | MR

[4] Bector, C. R., Chandra, S.: Fuzzy Mathematical Programming and Fuzzy Matrix Games. Springer-Verlag, Berlin 2005. | DOI | Zbl

[5] Cook, W. D.: Zero-sum games with multiple goals. Naval Research Logistics Quarterly 23 (1976), 615-622. | DOI | MR | Zbl

[6] Corley, S. C.: Games with vector payoffs. J. Optim. Theory Appl. 47 (1985), 463-475. | DOI | MR | Zbl

[7] Fernandez, F. R., Puerto, J.: Vector linear programming in zero-sum multicriteria matrix games. J. Optim. Theory Appl. 89 (1996), 115-127. | DOI | MR | Zbl

[8] Ghose, D., Prasad, U. R.: A solution concepts in two-person multicriteria games. J. Optim. Theory Appl. 63 (1989), 167-189. | DOI | MR

[9] Gaskó, N., Suciu, M., Lung, R. I., Dumitrescu, D.: Pareto-optimal Nash equilibrium detection using an evolutionary approach. Acta Univ. Sapientiae 4 (2012), 2, 237-246.

[10] Mavrotas, G.: Generation of Efficient Solutions in Multiobjective Mathematical Programming Problems Using GAMS. Effective Implementation of the $\epsilon$-constraint Method. Technical Report: http://www.gams.com/modlib/adddocs/epscm.pdf (2007), 167-189.

[11] Nishizaki, I., Sakawa, M.: Fuzzy and Multiobjective Games for Conflict Resolution. Kluwer Academic Publishers 2003. | DOI | Zbl

[12] Sakawa, M., Nishizaki, I.: Max-min solutions for fuzzy multi-objective mattrix games. Fuzzy Sets and Systems 67 (1994), 53-69. | DOI | MR

[13] Steuer, R. E.: Multiple Criteria Optimization: Theory, Computation and Application. John Wiley, New York 1986. | MR | Zbl

[14] Shapely, L. S.: Equilibirum points in games with vector payoff. Naval Research Logistics Quarterly 6 (1959), 57-61. | DOI | MR

[15] Vijay, V., Mehra, A., Chandra, S., Bector, C. R.: Fuzzy matrix games via a fuzzy relation approach. Fuzzy Optim. Decision Making 6 (2007), 299-314. | DOI | MR | Zbl

[16] Zeleny, M.: Games with multiple payoff. Int. J. Game Theory 4 (1975), 179-191. | DOI | MR

[17] Zimmermann, H. J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems1 (1978), 45-55. | DOI | MR | Zbl

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