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Intuitionistic fuzzy linear programming and duality: a level sets approach

Author

Listed:
  • Jaroslav Ramík

    (Silesian University)

  • Milan Vlach

    (Charles University in Prague)

Abstract

The paper is concerned with linear programming problems whose input data may be intuitionistic fuzzy (IF) while the values of variables are always real numbers. We propose rather general approach to this type of problems based on level sets, and present recent results for problems in which the notions of feasibility and optimality are based on the IF relations. Special attention is devoted to the weak and strong duality.

Suggested Citation

  • Jaroslav Ramík & Milan Vlach, 2016. "Intuitionistic fuzzy linear programming and duality: a level sets approach," Fuzzy Optimization and Decision Making, Springer, vol. 15(4), pages 457-489, December.
    • Handle: RePEc:spr:fuzodm:v:15:y:2016:i:4:d:10.1007_s10700-016-9233-0
    DOI: 10.1007/s10700-016-9233-0
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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. Stanciulescu, C. & Fortemps, Ph. & Installe, M. & Wertz, V., 2003. "Multiobjective fuzzy linear programming problems with fuzzy decision variables," European Journal of Operational Research, Elsevier, vol. 149(3), pages 654-675, September.
    3. David J. Thuente, 1980. "Technical Note—Duality Theory for Generalized Linear Programs with Computational Methods," Operations Research, INFORMS, vol. 28(4), pages 1005-1011, August.
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    Cited by:

    1. P. Senthil Kumar, 2024. "An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(9), pages 4370-4403, September.
    2. Yanan Zhang & Zhaopeng Meng & Yan Zheng & Anca Ralescu, 2019. "Schedule optimization under fuzzy constraints of vehicle capacity," Fuzzy Optimization and Decision Making, Springer, vol. 18(2), pages 131-150, June.
    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. Pedro Huidobro & Pedro Alonso & Vladimír Janiš & Susana Montes, 2022. "Convexity and level sets for interval-valued fuzzy sets," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 553-580, December.
    5. P. Senthil Kumar, 2019. "PSK Method for Solving Mixed and Type-4 Intuitionistic Fuzzy Solid Transportation Problems," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 10(2), pages 20-53, April.

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