Interval programming models for matrix games with interval payoffs

Optimization Methods and Software

Volumn 27, Issue 1, 2012, Pages 1-16

  Li, Deng Feng ^a   Nan, Jiang Xia ^b   Zhang, Mao Jun ^c  

^a FUZHOU UNIVERSITY   (China)

^b DALIAN UNIVERSITY   (China)

^c DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

interval; matrix game; multiobjective programming; optimization; uncertainty mathematical theory

Indexed keywords

FUZZY RANKINGS; INTERVAL; LINEAR PROGRAMMING MODELS; MATHEMATICAL THEORY; MATRIX GAME; MULTIOBJECTIVE PROGRAMMING; NUMERICAL EXAMPLE; PROGRAMMING MODELS;

COMPUTER PROGRAMMING; FUZZY SETS; OPTIMIZATION;

GAME THEORY;

EID: 84862912933     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556781003796622     Document Type: Article

References (28)

1. Z.M. Avsar and M.B. Gürsoy, A note on two-person zero-sum communicating stochastic games, Oper. Res. Lett. 34 (2006), pp. 412-420.
2. C.R. Bector and S. Chandra, Fuzzy Mathematical Programming and Fuzzy Matrix Games, Springer Verlag, Berlin, 2005.
3. C.R. Bector, S. Chandra, andV.Vijay, Duality in linear programming with fuzzy parameters and matrix games with fuzzy pay-offs, Fuzzy Sets Syst. 46(2) (2004), pp. 253-269.
4. C.R. Bector, S. Chandra, and V. Vijay, Matrix games with fuzzy goals and fuzzy linear programming duality, Fuzzy Optim. Decis. Mak. 3 (2004), pp. 255-269.
5. L. Campos, Fuzzy linear programming models to solve fuzzy matrix games, Fuzzy Sets Syst. 32 (1989), pp. 275-289.
6. S. Chanas and D.Kuchta, Multiobjective programming in optimization of interval objective functions-A generalized approach, Eur. J. Oper. Res. 94 (1996), pp. 594-598. (Pubitemid 126391964)
7. W.D. Collins and C.Y. Hu, Studying interval valued matrix games with fuzzy logic, Soft Comput. 12 (2008), pp. 147-155. (Pubitemid 47412746)
8. J.H. Dshalalow andW.J. Huang, On noncooperative hybrid stochastic games, Nonlinear Anal. Hybrid Syst. 2 (2008), pp. 803-811.
9. C.Y. Hu, R.B. Kearfott, A.D. Korvin, and V. Kreinovich, Knowledge Processing with Interval and Soft Computing, Springer Verlag, London, 2008, pp.168-172.
10. H. Ishibuchi and H. Tanaka, Multiobjective programming in optimization of the interval objective function, Eur. J. Oper. Res. 48 (1990), pp. 219-225.
11. G.R. Jahanshahloo, F. Hosseinzadeh Lotfi, and A.R. Davoodi, Extension of TOPSIS for decision-making problems with interval data: Interval efficiency, Math. Comput. Model. 49 (2009), pp. 1137-1142.
12. M. Larbani, Non cooperative fuzzy games in normal form: A survey, Fuzzy Sets Syst. 160 (2009), pp. 3184-3210.
13. D.F. Li, A fuzzy multiobjective programming approach to solve fuzzy matrix games, J. Fuzzy Math. 7(4) (1999), pp. 907-912.
14. D.F. Li, Fuzzy constrained matrix games with fuzzy payoffs, J. Fuzzy Math. 7(4) (1999), pp. 873-880.
15. D.F. Li, Fuzzy Multiobjective Many Person Decision Makings and Games, National Defense Industry Press, Beijing, 2003, pp. 196-326.
16. D.F. Li, Lexicographic method for matrix games with payoffs of triangular fuzzy numbers, Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 16(3) (2008), pp. 371-389.
17. D.F. Li and C.T. Cheng, Fuzzy multiobjective programming methods for fuzzy constrained matrix games with fuzzy numbers, Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 10(4) (2002), pp. 385-400.
18. D.F. Li and J.X. Nan, A nonlinear programming approach to matrix games with payoffs of Atanassov's intuitionistic fuzzy sets, Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 17(4) (2009), pp. 585-607.
19. S.T. Liu and C. Kao, Matrix games with interval data, Comput. Ind. Eng. 56 (2009), pp.1697-1700.
20. R.E. Moore, Method and Application of Interval Analysis, SIAM, Philadelphia, 1979.
21. P.K. Nayak and M. Pal, Linear programming technique to solve two person matrix games with interval pay-offs, Asia-Pac. J. Oper. Res. 26(2) (2009), pp. 285-305.
22. I. Nishizaki and M. Sakawa, Fuzzy and Multiobjective Games for Conflict Resolution, Physica-Verlag, Heidelberg, 2001.
23. A. Sengupta and T.K. Pal, Theory and methodology on comparing interval numbers, Eur. J. Oper. Res. 127 (2000), pp. 28-43.
24. A. Sengupta, T.K. Pal, and D. Chakraborty, Interpretation of inequality constraints involving interval coefficients and a solution to interval programming, Fuzzy Sets Syst. 119 (2001), pp. 129-138. (Pubitemid 32091794)
25. P. Sevastianov, Numerical methods for interval and fuzzy number comparison based on the probabilistic approach and Dempster-Shafer theory, Inf. Sci. 177 (2007), pp. 4645-4661. (Pubitemid 47238788)
26. J. Suijs, P. Borm, A.D.Waegenaere, and S. Tijs, Theory and methodology cooperative games with stochastic payoffs, Eur. J. Oper. Res. 113 (1999), pp. 193-205.
27. S. Tong, Interval number and fuzzy number linear programming, Fuzzy Sets Syst. 66 (1994), pp. 301-306.
28. Q. Zhang, Q.S. Gao, and J.H. Geng, New approach to multiple attribute decision making with interval numbers, J. Syst. Eng. Electron. 19 (2008), pp. 304-310.