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Solving Fuzzy Linear Programming Problems with Fuzzy Decision Variables

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  • Hsien-Chung Wu

    (Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan)

Abstract

The numerical method for solving the fuzzy linear programming problems with fuzzy decision variables is proposed in this paper. The difficulty for solving this kind of problem is that the decision variables are assumed to be nonnegative fuzzy numbers instead of nonnegative real numbers. In other words, the decision variables are assumed to be membership functions. One of the purposes of this paper is to derive the analytic formula of error estimation regarding the approximate optimal solution. On the other hand, the existence of optimal solutions is also studied in this paper. Finally we present two numerical examples to demonstrate the usefulness of the numerical method.

Suggested Citation

  • Hsien-Chung Wu, 2019. "Solving Fuzzy Linear Programming Problems with Fuzzy Decision Variables," Mathematics, MDPI, vol. 7(7), pages 1-105, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:569-:d:242946
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    References listed on IDEAS

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    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. 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.
    3. U. M. Pirzada & V. D. Pathak, 2013. "Newton Method for Solving the Multi-Variable Fuzzy Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 867-881, March.
    4. Dipankar Chakraborty & Dipak Kumar Jana & Tapan Kumar Roy, 2016. "A new approach to solve fully fuzzy transportation problem using triangular fuzzy number," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 26(2), pages 153-179.
    5. Wu, Hsien-Chung, 2009. "The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 49-60, July.
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    Cited by:

    1. Figueroa–García, Juan Carlos & Hernández, Germán & Franco, Carlos, 2022. "A review on history, trends and perspectives of fuzzy linear programming," Operations Research Perspectives, Elsevier, vol. 9(C).

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