| Title:
|
A necessity measure optimization approach to linear programming problems with oblique fuzzy vectors (English) |
| Author:
|
Inuiguchi, Masahiro |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
42 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
441-452 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, a necessity measure optimization model of linear programming problems with fuzzy oblique vectors is discussed. It is shown that the problems are reduced to linear fractional programming problems. Utilizing a special structure of the reduced problem, we propose a solution algorithm based on Bender’s decomposition. A numerical example is given. (English) |
| Keyword:
|
fuzzy linear programming |
| Keyword:
|
oblique fuzzy vector |
| Keyword:
|
necessity measure |
| Keyword:
|
Bender’s decomposition |
| MSC:
|
49M27 |
| MSC:
|
90C05 |
| MSC:
|
90C70 |
| idZBL:
|
Zbl 1249.90350 |
| idMR:
|
MR2275346 |
| . |
| Date available:
|
2009-09-24T20:17:24Z |
| Last updated:
|
2015-03-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135726 |
| . |
| Reference:
|
[1] Inuiguchi M.: Necessity optimization in linear programming problems with interactive fuzzy numbers.In: Proc. 7th Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty (H. Noguchi, H. Ishii and M. Inuiguchi, eds.), Awaji Yumebutai ICC, 2004, pp. 9–14 |
| Reference:
|
[2] Inuiguchi M., Ramík J.: Possibilistic linear programming: A brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem.Fuzzy Sets and Systems 111 (2000), 1, 3–28 Zbl 0938.90074, MR 1748690 |
| Reference:
|
[3] Inuiguchi M., Ramík, J., Tanino T.: Oblique fuzzy vectors and their use in possibilistic linear programming.Fuzzy Sets and Systems 137 (2003), 1, 123–150 Zbl 1026.90104, MR 1977539 |
| Reference:
|
[4] Inuiguchi M., Sakawa M.: A possibilistic linear program is equivalent to a stochastic linear program in a special case.Fuzzy Sets and Systems 76 (1995), 309–318 Zbl 0856.90131, MR 1365398 |
| Reference:
|
[5] Inuiguchi M., Tanino T.: Portfolio selection under independent possibilistic information.Fuzzy Sets and Systems 115 (2000), 1, 83–92 Zbl 0982.91028, MR 1776308 |
| Reference:
|
[6] Inuiguchi M., Tanino T.: Possibilistic linear programming with fuzzy if-then rule coefficients.Fuzzy Optimization and Decision Making 1 (2002), 1, 65–91 Zbl 1056.90142, MR 1922355, 10.1023/A:1013727809532 |
| Reference:
|
[7] Inuiguchi M., Tanino T.: Fuzzy linear programming with interactive uncertain parameters.Reliable Computing 10 (2004), 5, 357–367 Zbl 1048.65062, MR 2063296, 10.1023/B:REOM.0000032118.34323.f2 |
| Reference:
|
[8] Lasdon L. S.: Optimization Theory for Large Systems.Macmillan, New York 1970 Zbl 0991.90001, MR 0337317 |
| Reference:
|
[9] Rommelfanger H., Kresztfalvi T.: Multicriteria fuzzy optimization based on Yager’s parameterized t-norm.Found. Computing and Decision Sciences 16 (1991), 2, 99–110 MR 1186955 |
| Reference:
|
[10] Zimmermann H.-J.: Applications of fuzzy set theory to mathematical programming.Inform. Sci. 36 (1985), 1–2, 29–58 Zbl 0578.90095, MR 0813764, 10.1016/0020-0255(85)90025-8 |
| . |
