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Fuzzy linear programming problems: models and solutions

  • Methodologies and Application
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Abstract

We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, \(\alpha \)-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately.

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Acknowledgements

The first author thanks the Research Council of Ferdowsi University of Mashhad; the second and third authors thank the Research Council of Sharif University of Technology; and the fourth author thanks the Research Council of Ghent University for supporting this work.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

    Reza Ghanbari

  2. Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, Iran

    Khatere Ghorbani-Moghadam & Nezam Mahdavi-Amiri

  3. Department of Mathematical Modelling, Statistics and Bioinformatics, Ghent University, Ghent, Belgium

    Bernard De Baets

Authors
  1. Reza Ghanbari
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  2. Khatere Ghorbani-Moghadam
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  3. Nezam Mahdavi-Amiri
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  4. Bernard De Baets
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Correspondence to Nezam Mahdavi-Amiri.

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Ghanbari, R., Ghorbani-Moghadam, K., Mahdavi-Amiri, N. et al. Fuzzy linear programming problems: models and solutions. Soft Comput 24, 10043–10073 (2020). https://doi.org/10.1007/s00500-019-04519-w

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