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Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers

Author

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  • Bogdana Stanojević

    (Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Belgrade, Serbia)

  • Milan Stanojević

    (Faculty of Organizational Sciences, University of Belgrade, Jove Ilića 154, 11000 Belgrade, Serbia)

  • Sorin Nădăban

    (Department of Mathematics and Computer Science, Aurel Vlaicu University of Arad, Elena Drăgoi 2, RO-310330 Arad, Romania)

Abstract

Optimization problems in the fuzzy environment are widely studied in the literature. We restrict our attention to mathematical programming problems with coefficients and/or decision variables expressed by fuzzy numbers. Since the review of the recent literature on mathematical programming in the fuzzy environment shows that the extension principle is widely present through the fuzzy arithmetic but much less involved in the foundations of the solution concepts, we believe that efforts to rehabilitate the idea of following the extension principle when deriving relevant fuzzy descriptions to optimal solutions are highly needed. This paper identifies the current position and role of the extension principle in solving mathematical programming problems that involve fuzzy numbers in their models, highlighting the indispensability of the extension principle in approaching this class of problems. After presenting the basic ideas in fuzzy optimization, underlying the advantages and disadvantages of different solution approaches, we review the main methodologies yielding solutions that elude the extension principle, and then compare them to those that follow it. We also suggest research directions focusing on using the extension principle in all stages of the optimization process.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1272-:d:566983
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Sorin Nădăban, 2022. "Fuzzy Logic and Soft Computing—Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921–2017)," Mathematics, MDPI, vol. 10(17), pages 1-3, September.

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