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Some duality results on linear programming problems with symmetric fuzzy numbers

Author

Listed:
  • S. H. Nasseri

    (Mazandaran University
    National Elite Foundation)

  • N. Mahdavi-Amiri

    (Sharif University of Technology)

Abstract

Recently, linear programming problems with symmetric fuzzy numbers (LPSFN) have considered by some authors and have proposed a new method for solving these problems without converting to the classical linear programming problem, where the cost coefficients are symmetric fuzzy numbers (see in [4]). Here we extend their results and first prove the optimality theorem and then define the dual problem of LPSFN problem. Furthermore, we give some duality results as a natural extensions of duality results for linear programming problems with crisp data.

Suggested Citation

  • S. H. Nasseri & N. Mahdavi-Amiri, 2009. "Some duality results on linear programming problems with symmetric fuzzy numbers," Fuzzy Information and Engineering, Springer, vol. 1(1), pages 59-66, March.
    • Handle: RePEc:spr:fuzinf:v:1:y:2009:i:1:d:10.1007_s12543-009-0004-2
    DOI: 10.1007/s12543-009-0004-2
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    References listed on IDEAS

    as
    1. K. Ganesan & P. Veeramani, 2006. "Fuzzy linear programs with trapezoidal fuzzy numbers," Annals of Operations Research, Springer, vol. 143(1), pages 305-315, March.
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    Cited by:

    1. S. H. Nasseri & E. Behmanesh, 2013. "Linear programming with triangular fuzzy numbers—A case study in a finance and credit institute," Fuzzy Information and Engineering, Springer, vol. 5(3), pages 295-315, September.
    2. A. Ebrahimnejad & S. H. Nasseri, 2009. "Using complementary slackness property to solve linear programming with fuzzy parameters," Fuzzy Information and Engineering, Springer, vol. 1(3), pages 233-245, September.
    3. Anila Gupta & Amit Kumar & Mahesh Kumar Sharma, 2013. "Applications of fuzzy linear programming with generalized LR flat fuzzy parameters," Fuzzy Information and Engineering, Springer, vol. 5(4), pages 475-492, December.
    4. Zeinab Kheiri & Faezeh Zahmatkesh & Bing-Yuan Cao, 2013. "New method to posynomial geometric programming of trapezoidal fuzzy numbers," Fuzzy Information and Engineering, Springer, vol. 5(3), pages 373-380, September.

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