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A Simplified Novel Technique for Solving Fully Fuzzy Linear Programming Problems

Author

Listed:
  • Izaz Ullah Khan

    (COMSATS Institute of IT Abbottabad
    Universiti Teknologi Malaysia)

  • Tahir Ahmad

    (Universiti Teknologi Malaysia)

  • Normah Maan

    (Universiti Teknologi Malaysia)

Abstract

This study proposes a novel technique for solving Linear Programming Problems in a fully fuzzy environment. A modified version of the well-known simplex method is used for solving fuzzy linear programming problems. The use of a ranking function together with the Gaussian elimination process helps in solving linear programming problems in a fully uncertain environment. The proposed algorithm is flexible, easy and reasonable.

Suggested Citation

  • Izaz Ullah Khan & Tahir Ahmad & Normah Maan, 2013. "A Simplified Novel Technique for Solving Fully Fuzzy Linear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 536-546, November.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:2:d:10.1007_s10957-012-0215-2
    DOI: 10.1007/s10957-012-0215-2
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    References listed on IDEAS

    as
    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. 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. Bogdana Stanojević & Milan Stanojević & Sorin Nădăban, 2021. "Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers," Mathematics, MDPI, vol. 9(11), pages 1-16, June.
    2. Izaz Ullah Khan & Tahir Ahmad & Normah Maan, 2017. "A Reply to a Note on the Paper “A Simplified Novel Technique for Solving Fully Fuzzy Linear Programming Problems”," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 353-356, April.
    3. Hawaf AbdAlhakim & O. E. Emam & A. A. Abd El-Mageed, 2019. "Architecting a fully fuzzy information model for multi-level quadratically constrained quadratic programming problem," OPSEARCH, Springer;Operational Research Society of India, vol. 56(2), pages 367-389, June.
    4. Arana-Jiménez, Manuel & Blanco, Víctor & Fernández, Elena, 2020. "On the fuzzy maximal covering location problem," European Journal of Operational Research, Elsevier, vol. 283(2), pages 692-705.
    5. Bogdana Stanojević & Milan Stanojević, 2016. "Parametric computation of a fuzzy set solution to a class of fuzzy linear fractional optimization problems," Fuzzy Optimization and Decision Making, Springer, vol. 15(4), pages 435-455, December.
    6. Hsien-Chung Wu, 2019. "Solving Fuzzy Linear Programming Problems with Fuzzy Decision Variables," Mathematics, MDPI, vol. 7(7), pages 1-105, June.
    7. Manuel Arana-Jiménez & Carmen Sánchez-Gil, 2020. "On generating the set of nondominated solutions of a linear programming problem with parameterized fuzzy numbers," Journal of Global Optimization, Springer, vol. 77(1), pages 27-52, May.

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