Cover
Vol. 6 No. 2 (2010)

Published: November 30, 2010

Pages: 89-96

Original Article

Proposed Method for Optimizing Fuzzy linear programming Problems by using Two-Phase Technique

Zaki S. Towfik 1 Sabiha Fathil Jawad
1Department of Computer Science Collage of Science University of AI-Mustansiriyah - Iraq
History
  • Received: September 30, 2010
  • Available Online: November 30, 2010
DOI

https://doi.org/10.37917/ijeee.6.2.2

Abstract

Fuzzy linear programming (FLP ) is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming contains fuzzy constrains or crisp objectives function or contains crisp constrains with fuzzy objectives function, which called fuzzy linear programming (FLP) with triplet fuzzy numbers consist a hybrid fuzzy. The crisp constrains used in the problems of types (= or ≥) with a proposed optimization fuzzy objectives and fuzzy constrains. In this paper proposed method for solving fuzzy linear programming problem by using Two-phase technique to solve the problem and to determine the optima crisp objectives.

Keywords

References

  1. Rafail N. Gasimov, Kürşat Yenilmez, "Solving Fuzzy Linear Programming Problems with Linear Membership Functions", 2002.
  2. Dubois, D., Prade, H., "System of Linear Fuzzy Constraints, Fuzzy Sets and Systems", 13 (1982), 1–10.
  3. Frank Rogers, J. Neggers, and Younbae Jun, "Method for Optimizing Linear Problems with Fuzzy Constraints", International Mathematical Forum, 3 (2008), no. 23, 1141–1155.
  4. Buckley and T. Feuring, "Evolutionary Algorithm Solution to Fuzzy Problems: Fuzzy Linear Programming, Fuzzy Sets and Systems", vol. 109 (2000), 35–53.
  5. G. Zhang, Y. H. Wu, M. Remias, and J. Lu, "Formulation of Fuzzy Linear Programming Problems as Four-Objective Constrained Optimization Problems", Applied Mathematics and Computation, vol. 139 (2003), 383–399.
  6. Shaocheng, T., "Interval Number and Fuzzy Number Linear Programming", Fuzzy Sets and Systems, 66 (1994), 301–306.
  7. H. R. Maleki, "Ranking Functions and Their Applications to Fuzzy Linear Programming", Far East Journal of Mathematical Sciences, vol. 4 (2002), 283–301.
  8. J. Ramik, "Duality in Fuzzy Linear Programming: Some New Concepts and Results", Fuzzy Optimization and Decision Making, vol. 4 (2005), 25–39.
  9. F. H. Lotfi, T. Allahviranloo, M. A. Jondabeh, and L. Alizadeh, "Solving a Fully Fuzzy Linear Programming Using Lexicography Method and Fuzzy Approximate Solution", Applied Mathematical Modeling, vol. 33 (2009), 3151–3156.
  10. S. H. Nasseri, "A New Method for Solving Fuzzy Linear Programming by Solving Linear Programming", Applied Mathematical Sciences, vol. 2 (2008), 2473–2480.
  11. S. M. Hashemi, M. Modarres, E. Nasrabadi, and M. M. Nasrabadi, "Fully Fuzzified Linear Programming: Solution and Duality", Journal of Intelligent and Fuzzy Systems, vol. 17 (2006), 253–261.
  12. M. Jimenez, M. Arenas, A. Bilbao, and M. V. Rodríguez, "Linear Programming with Fuzzy Parameters: An Interactive Method Resolution", European Journal of Operational Research, vol. 177 (2007), 1599–1609.
  13. H. R. Maleki, "Ranking Functions and Their Applications to Fuzzy Linear Programming", Far East Journal of Mathematical Sciences, 4 (2002), 283–301.