| Title:
|
Solving multi-objective fuzzy matrix games via multi-objective linear programming approach (English) |
| Author:
|
Aggarwal, Abha |
| Author:
|
Khan, Imran |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
52 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
153-168 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
multi-objective game |
| Keyword:
|
Pareto-optimal security strategies |
| Keyword:
|
security level |
| Keyword:
|
multi-objective linear programming |
| MSC:
|
90C70 |
| MSC:
|
91A40 |
| idZBL:
|
Zbl 06562218 |
| idMR:
|
MR3482616 |
| DOI:
|
10.14736/kyb-2016-1-0153 |
| . |
| Date available:
|
2016-03-21T17:57:57Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144868 |
| . |
| Reference:
|
[1] Bellman, R. E., Zadeh, L. A.: Decision making in a fuzzy environment..Management Sci. 17 (1970), 141-164. Zbl 0224.90032, MR 0301613, 10.1287/mnsc.17.4.b141 |
| Reference:
|
[2] Blackwell, D.: An analog of the minimax theorem for vector payoff..Pacific J. Math. 6 (1956), 1-8. MR 0081804, 10.2140/pjm.1956.6.1 |
| Reference:
|
[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. MR 2102800, 10.1023/b:fodm.0000036866.18909.f1 |
| Reference:
|
[4] Bector, C. R., Chandra, S.: Fuzzy Mathematical Programming and Fuzzy Matrix Games..Springer-Verlag, Berlin 2005. Zbl 1078.90071, 10.1007/3-540-32371-6 |
| Reference:
|
[5] Cook, W. D.: Zero-sum games with multiple goals..Naval Research Logistics Quarterly 23 (1976), 615-622. Zbl 0371.90125, MR 0444058, 10.1002/nav.3800230406 |
| Reference:
|
[6] Corley, S. C.: Games with vector payoffs..J. Optim. Theory Appl. 47 (1985), 463-475. Zbl 0556.90095, MR 0818874, 10.1007/bf00942194 |
| Reference:
|
[7] Fernandez, F. R., Puerto, J.: Vector linear programming in zero-sum multicriteria matrix games..J. Optim. Theory Appl. 89 (1996), 115-127. Zbl 0866.90139, MR 1382533, 10.1007/bf02192644 |
| Reference:
|
[8] Ghose, D., Prasad, U. R.: A solution concepts in two-person multicriteria games..J. Optim. Theory Appl. 63 (1989), 167-189. MR 1026863, 10.1007/bf00939572 |
| Reference:
|
[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. |
| Reference:
|
[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. |
| Reference:
|
[11] Nishizaki, I., Sakawa, M.: Fuzzy and Multiobjective Games for Conflict Resolution..Kluwer Academic Publishers 2003. Zbl 0973.91001, 10.1007/978-3-7908-1830-7 |
| Reference:
|
[12] Sakawa, M., Nishizaki, I.: Max-min solutions for fuzzy multi-objective mattrix games..Fuzzy Sets and Systems 67 (1994), 53-69. MR 1300301, 10.1016/0165-0114(94)90208-9 |
| Reference:
|
[13] Steuer, R. E.: Multiple Criteria Optimization: Theory, Computation and Application..John Wiley, New York 1986. Zbl 0742.90068, MR 0836977 |
| Reference:
|
[14] Shapely, L. S.: Equilibirum points in games with vector payoff..Naval Research Logistics Quarterly 6 (1959), 57-61. MR 0109748, 10.1002/nav.3800060107 |
| Reference:
|
[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. Zbl 1151.91319, MR 2365211, 10.1007/s10700-007-9015-9 |
| Reference:
|
[16] Zeleny, M.: Games with multiple payoff..Int. J. Game Theory 4 (1975), 179-191. MR 0401181, 10.1007/bf01769266 |
| Reference:
|
[17] Zimmermann, H. J.: Fuzzy programming and linear programming with several objective functions..Fuzzy Sets and Systems1 (1978), 45-55. Zbl 0548.90076, MR 0496734, 10.1016/0165-0114(78)90031-3 |
| . |
