A necessity measure optimization approach to linear programming problems with oblique fuzzy vectors

Masahiro Inuiguchi

Kybernetika (2006)

  • Volume: 42, Issue: 4, page 441-452
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Inuiguchi, Masahiro. "A necessity measure optimization approach to linear programming problems with oblique fuzzy vectors." Kybernetika 42.4 (2006): 441-452. <http://eudml.org/doc/33816>.

@article{Inuiguchi2006,
abstract = {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.},
author = {Inuiguchi, Masahiro},
journal = {Kybernetika},
keywords = {fuzzy linear programming; oblique fuzzy vector; necessity measure; Bender’s decomposition; fuzzy linear programming; oblique fuzzy vector; necessity measure; Bender's decomposition},
language = {eng},
number = {4},
pages = {441-452},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A necessity measure optimization approach to linear programming problems with oblique fuzzy vectors},
url = {http://eudml.org/doc/33816},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Inuiguchi, Masahiro
TI - A necessity measure optimization approach to linear programming problems with oblique fuzzy vectors
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 4
SP - 441
EP - 452
AB - 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.
LA - eng
KW - fuzzy linear programming; oblique fuzzy vector; necessity measure; Bender’s decomposition; fuzzy linear programming; oblique fuzzy vector; necessity measure; Bender's decomposition
UR - http://eudml.org/doc/33816
ER -

References

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  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 
  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 Zbl0938.90074MR1748690
  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 Zbl1026.90104MR1977539
  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 (1995) Zbl0856.90131MR1365398
  5. Inuiguchi M., Tanino T., Portfolio selection under independent possibilistic information, Fuzzy Sets and Systems 115 (2000), 1, 83–92 Zbl0982.91028MR1776308
  6. Inuiguchi M., Tanino T., 10.1023/A:1013727809532, Fuzzy Optimization and Decision Making 1 (2002), 1, 65–91 Zbl1056.90142MR1922355DOI10.1023/A:1013727809532
  7. Inuiguchi M., Tanino T., 10.1023/B:REOM.0000032118.34323.f2, Reliable Computing 10 (2004), 5, 357–367 Zbl1048.65062MR2063296DOI10.1023/B:REOM.0000032118.34323.f2
  8. Lasdon L. S., Optimization Theory for Large Systems, Macmillan, New York 1970 Zbl0991.90001MR0337317
  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 (1991) MR1186955
  10. Zimmermann H.-J., 10.1016/0020-0255(85)90025-8, Inform. Sci. 36 (1985), 1–2, 29–58 (1985) Zbl0578.90095MR0813764DOI10.1016/0020-0255(85)90025-8

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