A lexicographic method for matrix games with payoffs of triangular intuitionistic fuzzy numbers

International Journal of Computational Intelligence Systems

Volumn 3, Issue 3, 2010, Pages 280-289

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

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^b DALIAN UNIVERSITY   (China)

^c FUZHOU UNIVERSITY   (China)

Author keywords

Intuitionistic fuzzy set; Lexicographic method; Mathematical programming; Matrix game; Triangular intuitionistic fuzzy number

Indexed keywords

ARITHMETIC OPERATIONS; CUT SETS; INTUITIONISTIC FUZZY; INTUITIONISTIC FUZZY NUMBER; INTUITIONISTIC FUZZY SETS; LEXICOGRAPHIC METHODS; LINEAR PROGRAMMING MODELS; MATRIX GAME; NUMERICAL EXAMPLE; ORDER RELATION;

FUZZY RULES; FUZZY SETS; MATHEMATICAL PROGRAMMING; MATRIX ALGEBRA; NUMERICAL METHODS;

GAME THEORY;

EID: 78650683924     PISSN: 18756891     EISSN: 18756883     Source Type: Journal    
DOI: 10.2991/ijcis.2010.3.3.4     Document Type: Article

References (32)

1. C. R. Bector and S. Chandra, Fuzzy Mathematical Programming and Fuzzy Matrix Games (Springer Verlag, Berlin, Germany, 2005).
2. C. R. Bector, S. Chandra and V. Vijay, Matrix games with fuzzy goals and fuzzy linear programming duality, Fuzzy Optimization and Decision Making 3 (2004) 255- 269.
3. C. R. Bector, S. Chandra and V. Vijay, Duality in linear programming with fuzzy parameters and matrix games with fuzzy pay-offs, Fuzzy Sets and Systems 46 (2) (2004) 253-269.
4. L. Campos, Fuzzy linear programming models to solve fuzzy matrix games, Fuzzy Sets and Systems 32 (1989) 275-289.
5. L. Campos and A. Gonzalez, Fuzzy matrix games considering the criteria of the players, Kybernetes 20 (1991) 17-23.
6. 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 and Systems 49 (1992) 193-203.
7. D. Dubois and H. Prade, Fuzzy Sets and Systems Theory and Applications (Academic Press, New York, 1980).
8. D. F. Li, Fuzzy Multiobjective Many Person Decision Makings and Games (National Defense Industry Press, Beijing, 2003).
9. D. F. Li, Fuzzy constrained matrix games with fuzzy payoffs, The Journal of Fuzzy Mathematics 7(4) (1999) 873-880.
10. D. F. Li, A fuzzy multiobjective programming approach to solve fuzzy matrix games, The Journal of Fuzzy Mathematics 7 (4) (1999) 907-912.
11. S. T. Liu and C. Kao, Solution of fuzzy matrix games: an application of the extension principle, International journal of intelligent systems 22 (2007) 891-903.
12. I. Nishizaki and M. Sakawa, Equilibrium solutions in multiobjective bimatrix games with fuzzy payoffs and fuzzy goals, Fuzzy Sets and Systems 111 (1) (2000) 99- 116.
13. I. Nishizaki and M. Sakawa, Solutions based on fuzzy goals in fuzzy linear programming games, Fuzzy Sets and Systems 115 (1) (2000) 105-119.
14. I. Nishizaki and M. Sakawa, Fuzzy and Multiobjective Games for Conflict Resolution (Physica-Verlag, Heidelberg, 2001).
15. M. Sakawa and I. Nishizaki, A lexicographical solution concept in an n-person cooperative fuzzy game, Fuzzy Sets and Systems 61 (1994) 265-275.
16. M. Sakawa and I. Nishizaki, Max-min solutions for fuzzy multiobjective matrix games, Fuzzy Sets and Systems 67 (1994) 53-69.
17. V. Vijay, S. Chandra and C. R. Bector, Matrix games with fuzzy goals and fuzzy payoffs, Omega 33 (2005) 425-429.
18. K. T. Atanassov, Intuitionistic Fuzzy Set (Springer-Verlag, Heidelberg, 1999).
19. S. K. De, R. Biswas and A. R. Roy, An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy Sets and Systems 117(2001) 209-213.
20. D. F. Li. and C. T. Cheng, New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions, Pattern Recognition Letters 23 (2002) 221-225.
21. D. F. Li, Multiattribute decision making models and methods using intuitionistic fuzzy sets, Journal of Computer and System Sciences 70 (2005) 73-85.
22. H. W. Liu and G. J.Wang, Multi-criteria decisionmaking methods based on intuitionistic fuzzy sets, European Journal of Operational Research 179 (2007) 220-233.
23. K. T. Atanassov, Ideas for intuitionistic fuzzy equations, inequalities and optimization, Notes on Intuitionistic Fuzzy Sets 1 (1) (1995) 17-24.
24. D. Dimitrov, Market Structure: An Intuitionistic Fuzzy Approach (Economy University Publishing House, Sofia, 2000).
25. D. Dimitrov, On intuitionistic fuzzy consent rules, Notes on Intuitionistic Fuzzy Sets 7 (4) (2001) 65-69.
26. D. F. Li and J. X. Nan, A nonlinear programming approach to matrix games with payoffs of Atanassov's intuitionistic fuzzy sets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17 (4) (2009) 585-607.
27. X. B. Li, D. Ruan, J. Liu and Y. Xu, A Linguistic-Valued Weighted Aggregation Operator to Multiple Attribute Group Decision Making with Quantative and Qualitative Information, International Journal of Computational Intelligence Systems 3(2008) 274 - 284.
28. L. A. Zadeh, Outline of a new approach to the analysis of complex systems and decision processes intervalvalued fuzzy sets, IEEE Transactions on Systems, Man, and Cybernetics 3 (1973) 28-44.
29. C. Kahraman and A. C. Tolga, An alternative ranking approach and its usage in multi-criteria decision-Making, International Journal of Computational Intelligence Systems 2(2009) 219 - 235.
30. D. F. Li, A note on using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly, Microelectronics Reliability 48 (2008)1741.
31. C. Kahraman, O. Engin and M. K. Yilmaz, A New Artificial Immune System Algorithm for Multiobjective Fuzzy Flow Shop Problems, International Journal of Computational Intelligence Systems 3 (2009) 236 - 247.
32. K. Shimizu, Y. Ishizuka and J. F. Bard, Nondifferentiable and Two-Level Mathematical Programming (Kluwer Academic Publishers, Boston, 1997).