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Applications of fuzzy linear programming with generalized LR flat fuzzy parameters

Author

Listed:
  • Anila Gupta

    (Shaheed Bhagat Singh State Technical Campus)

  • Amit Kumar

    (Thapar University)

  • Mahesh Kumar Sharma

    (Thapar University)

Abstract

In this paper, the limitations of existing methods to solve the problems of fuzzy assignment, fuzzy travelling salesman and fuzzy generalized assignment are pointed out. All these problems can be formulated in linear programming problems wherein the decision variables are represented by real numbers and other parameters are represented by fuzzy numbers. To overcome the limitations of existing methods, a new method is proposed. The advantage of proposed method over existing methods is demonstrated by solving the problems mentioned above which can or cannot be solved by using the existing methods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:fuzinf:v:5:y:2013:i:4:d:10.1007_s12543-013-0159-8
    DOI: 10.1007/s12543-013-0159-8
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    References listed on IDEAS

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    1. A. Ebrahimnejad & S.H. Nasseri & F. Hosseinzadeh Lotfi & M. Soltanifar, 2010. "A primal-dual method for linear programming problems with fuzzy variables," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 4(2), pages 189-209.
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    3. S.H. Nasseri & A. Ebrahimnejad, 2010. "A fuzzy primal simplex algorithm and its application for solving flexible linear programming problems," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 4(3), pages 372-389.
    4. A. Ebrahimnejad & Seyed Hadi Nasseri, 2010. "A dual simplex method for bounded linear programmes with fuzzy numbers," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 2(6), pages 762-779.
    5. Ali Ebrahimnejad & Seyed Hadi Nasseri & Sayyed Mehdi Mansourzadeh, 2011. "Bounded Primal Simplex Algorithm for Bounded Linear Programming with Fuzzy Cost Coefficients," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 2(1), pages 96-120, January.
    6. 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.
    7. 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.
    8. Amit Kumar & Pushpinder Singh & Amarpreet Kaur & Parmpreet Kaur, 2010. "RM approach for ranking of generalized trapezoidal fuzzy numbers," Fuzzy Information and Engineering, Springer, vol. 2(1), pages 37-47, March.
    Full references (including those not matched with items on IDEAS)

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