Previous |  Up |  Next


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:
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


Files Size Format View
Kybernetika_42-2006-4_4.pdf 834.3Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo