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Empiric Solutions to Full Fuzzy Linear Programming Problems Using the Generalized “min” Operator

Author

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  • Bogdana Stanojević

    (Mathematical Institute of the Serbian Academy of Sciences and Arts, 11000 Belgrade, Serbia)

  • Sorin Nǎdǎban

    (Department of Mathematics and Computer Science, Aurel Vlaicu University of Arad, RO-310330 Arad, Romania)

Abstract

Solving optimization problems in a fuzzy environment is an area widely addressed in the recent literature. De-fuzzification of data, construction of crisp more or less equivalent problems, unification of multiple objectives, and solving a single crisp optimization problem are the general descriptions of many procedures that approach fuzzy optimization problems. Such procedures are misleading (since relevant information is lost through de-fuzzyfication and aggregation of more objectives into a single one), but they are still dominant in the literature due to their simplicity. In this paper, we address the full fuzzy linear programming problem, and provide solutions in full accordance with the extension principle. The main contribution of this paper is in modeling the conjunction of the fuzzy sets using the “product” operator instead of “min” within the definition of the solution concept. Our theoretical findings show that using a generalized “min” operator within the extension principle assures thinner shapes to the derived fuzzy solutions compared to those available in the literature. Thinner shapes are always desirable, since such solutions provide the decision maker with more significant information.

Suggested Citation

  • Bogdana Stanojević & Sorin Nǎdǎban, 2023. "Empiric Solutions to Full Fuzzy Linear Programming Problems Using the Generalized “min” Operator," Mathematics, MDPI, vol. 11(23), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4864-:d:1293610
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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. Liu, Shiang-Tai & Kao, Chiang, 2004. "Solving fuzzy transportation problems based on extension principle," European Journal of Operational Research, Elsevier, vol. 153(3), pages 661-674, March.
    3. Ali Ebrahimnejad & Jose Luis Verdegay, 2018. "A new approach for solving fully intuitionistic fuzzy transportation problems," Fuzzy Optimization and Decision Making, Springer, vol. 17(4), pages 447-474, December.
    4. 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.
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