FUZZY MATRİS OYUNLARIN ÇÖZÜMLERİ ÜZERİNE

Öz

In this paper a two person zero-sum game with fuzzy goals and fuzzy payoffs are considered and their solutions

are calculated using a suitable defuzzification function and Sakawa’s method. Then we compared solutions of the

given an example. We have used MAPLE 12 computer algebra system to solve given problem.

Anahtar Kelimeler

• Fuzzy goal,Fuzzy payoff,Two person zero-sum game,Fuzzy payoff matrix,Fuzzy number

FUZZY MATRİS OYUNLARIN ÇÖZÜMLERİ ÜZERİNE

Öz

Bu makalede fuzzy hedefli ve fuzzy ödemeli iki kişili sıfır toplamlı oyunlar ele alındı ve oyunun çözümleri için uygun bir defüzifikasyon fonksiyonu metodu ve Sakawa’nın metodu tanıtıldı. Örnek üzerinde yöntemler incelenerek sonuçlar karşılaştırıldı.

Anahtar Kelimeler

• Fuzzy hedef,Fuzzy ödeme,İki kişili sıfır toplamlı oyun,Fuzzy ödemeli matris,Fuzzy sayı

Kaynakça

1. [1] Sakawa, M. and. Nishizaki, I, Max-Min solutions for fuzzy multiobjective matrix games, Fuzzy set and Systems, Vol.67, pp.53-69, 1994.
2. [2] Shimizu K. and Aiyoshi E., Necessary conditions for min-max problems and algorithm by a relaxation procedure, IEEE Trans. Automat. Control AC-25, 62-66 ,1980
3. [3] Charnes A. and Cooper W., Programming with linear fractional function, Naval Res. Logist. Quart. 9, 181-186, 1962
4. [4] Nishizaki I; Sakawa M, Fuzzy and Multiobjective Games for Conflict Resolution, Heidelberg; New York: Physica-Verl., 2001
5. [5] Cook W.D., Zero-sum games with multiple goals, Naval Res. Logist. Quart. 23, 615-622 1976
6. [6] Zeleny M., Games with multiple payoffs, International Journal of Game Theory, Vol.4, pp. 179-191, 1975.
7. [7].Campos L, Fuzzy linear programming models to solve fuzzy matrix games, Fuzzy Sets and Systems, Vol.32, pp.275-289, 1989
8. [8] Vijay V.,:Chandra S,.Bector C.R, Matrix games with fuzzy goals and fuzzy payoffs, Omega, Vol.33, pp. 425-429, 2005

9. [9] Sakawa M., Interactive computer program for fuzzy linear programming with multiple objectives, International journal of man-machine studies, Vol.18, pp.489-503, 1983.
10. [10].Yager R.R, A procedure for ordering fuzzy numbers of the unit interval, Information Sciences, Vol.24, pp.143-161, 1981
11. [11].Zimmermann H.J, fuzzy programming and linear programming with several objective functions, Fuzzy sets and systems, Vol.1, pp.45-55, 1978
12. [12] Aubin J.P. Mathematical Methods of Game and Economic Theory 1979
13. [13] Aubin J.P. Cooperative fuzzy game, Math. Of Oper. Res. 6 1-13, 1981
14. [14] Butnariu D. Fuzzy games : A description of the concept, Fuzzy sets and systems 1, 181-192, 1978
15. [15] Butnariu D. Stability and shapley value for n-person fuzzy game, Fuzzy sets and systems 4, 63-72, 1980
16. [16] Bector C.R.,Chandra S. On duality in linear programming under fuzzy environment, Fuzzy sets and systems 125:3, 17-25, 2002
17. [17] Bector C.R.,Chandra S.,Vijay V., Matrix games with fuzzy goals and fuzzy linear programming duality, Fuzzy Optimization and Decision Making 3:2 55-69, 2004
18. [18] Bector C.R.,Chandra S., Vijay V, Duality in linear programming with fuzzy parameters and matrix games with fuzzy payoffs, Fuzzy sets and systems 146:2, 53-69, 2004
19. [19] Maeda T., On characterization of equilibrium strategy of two person zero-sum games with fuzzy payoffs, Fuzzy sets and systems 139:2, 83-96, 2003
20. [20] Li D-F. A fuzzy multiobjective approach to solve fuzzy matrix games, The journal of Fuzzy Mathematics 7:907-12, 1999