FUZZY MATRİS OYUNLARIN ÇÖZÜMLERİ ÜZERİNE
Year 2010,
Issue: 021, 25 - 36, 15.04.2010
Adem Cengiz Çevikel
,
Mehmet Ahlatçıoğlu
Abstract
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.
References
- [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] 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] Charnes A. and Cooper W., Programming with linear fractional function, Naval Res. Logist. Quart. 9, 181-186, 1962
- [4] Nishizaki I; Sakawa M, Fuzzy and Multiobjective Games for Conflict Resolution, Heidelberg; New York: Physica-Verl., 2001
- [5] Cook W.D., Zero-sum games with multiple goals, Naval Res. Logist. Quart. 23, 615-622 1976
- [6] Zeleny M., Games with multiple payoffs, International Journal of Game Theory, Vol.4, pp. 179-191, 1975.
- [7].Campos L, Fuzzy linear programming models to solve fuzzy matrix games, Fuzzy Sets and Systems, Vol.32, pp.275-289, 1989
- [8] Vijay V.,:Chandra S,.Bector C.R, Matrix games with fuzzy goals and fuzzy payoffs, Omega, Vol.33, pp. 425-429, 2005
- [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].Yager R.R, A procedure for ordering fuzzy numbers of the unit interval, Information Sciences, Vol.24, pp.143-161, 1981
- [11].Zimmermann H.J, fuzzy programming and linear programming with several objective functions, Fuzzy sets and systems, Vol.1, pp.45-55, 1978
- [12] Aubin J.P. Mathematical Methods of Game and Economic Theory 1979
- [13] Aubin J.P. Cooperative fuzzy game, Math. Of Oper. Res. 6 1-13, 1981
- [14] Butnariu D. Fuzzy games : A description of the concept, Fuzzy sets and systems 1, 181-192, 1978
- [15] Butnariu D. Stability and shapley value for n-person fuzzy game, Fuzzy sets and systems 4, 63-72, 1980
- [16] Bector C.R.,Chandra S. On duality in linear programming under fuzzy environment, Fuzzy sets and systems 125:3, 17-25, 2002
- [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] 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] 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] Li D-F. A fuzzy multiobjective approach to solve fuzzy matrix games, The journal of Fuzzy Mathematics 7:907-12, 1999
FUZZY MATRİS OYUNLARIN ÇÖZÜMLERİ ÜZERİNE
Year 2010,
Issue: 021, 25 - 36, 15.04.2010
Adem Cengiz Çevikel
,
Mehmet Ahlatçıoğlu
Abstract
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.
References
- [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] 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] Charnes A. and Cooper W., Programming with linear fractional function, Naval Res. Logist. Quart. 9, 181-186, 1962
- [4] Nishizaki I; Sakawa M, Fuzzy and Multiobjective Games for Conflict Resolution, Heidelberg; New York: Physica-Verl., 2001
- [5] Cook W.D., Zero-sum games with multiple goals, Naval Res. Logist. Quart. 23, 615-622 1976
- [6] Zeleny M., Games with multiple payoffs, International Journal of Game Theory, Vol.4, pp. 179-191, 1975.
- [7].Campos L, Fuzzy linear programming models to solve fuzzy matrix games, Fuzzy Sets and Systems, Vol.32, pp.275-289, 1989
- [8] Vijay V.,:Chandra S,.Bector C.R, Matrix games with fuzzy goals and fuzzy payoffs, Omega, Vol.33, pp. 425-429, 2005
- [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].Yager R.R, A procedure for ordering fuzzy numbers of the unit interval, Information Sciences, Vol.24, pp.143-161, 1981
- [11].Zimmermann H.J, fuzzy programming and linear programming with several objective functions, Fuzzy sets and systems, Vol.1, pp.45-55, 1978
- [12] Aubin J.P. Mathematical Methods of Game and Economic Theory 1979
- [13] Aubin J.P. Cooperative fuzzy game, Math. Of Oper. Res. 6 1-13, 1981
- [14] Butnariu D. Fuzzy games : A description of the concept, Fuzzy sets and systems 1, 181-192, 1978
- [15] Butnariu D. Stability and shapley value for n-person fuzzy game, Fuzzy sets and systems 4, 63-72, 1980
- [16] Bector C.R.,Chandra S. On duality in linear programming under fuzzy environment, Fuzzy sets and systems 125:3, 17-25, 2002
- [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] 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] 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] Li D-F. A fuzzy multiobjective approach to solve fuzzy matrix games, The journal of Fuzzy Mathematics 7:907-12, 1999