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Duality theory in Atanassov’s intuitionistic fuzzy mathematical programming problems: Optimistic, pessimistic and mixed approaches

Author

Listed:
  • Vishnu Singh

    (Indian Institute of Technology Roorkee)

  • Shiv Prasad Yadav

    (Indian Institute of Technology Roorkee)

  • Sujeet Kumar Singh

    (The Logistics Institute-Asia Pacific, National University of Singapore)

Abstract

Linear programming problems in fuzzy environment have been investigated by many researchers in the recent years. Some researchers have solved these problems by using primal-dual method with linear and exponential membership functions. These membership functions are particular form of the reference functions. In this paper, we introduce a pair of primal-dual PPs in Atanassov’s intuitionistic fuzzy environment (AIFE) in which the membership and non-membership functions are taken in the form of the reference functions and prove duality results in AIFE by using an aspiration level approach with different view points, viz., optimistic, pessimistic and mixed. Since fuzzy and AIF environments cause duality gap, we propose to investigate the impact of membership functions governed by reference functions on duality gap. This is specially meaningful for fuzzy and AIF programming problems, when the primal and dual objective values may not be bounded. Finally, the duality gap obtained by the approach has been compared with the duality gap obtained by existing approaches.

Suggested Citation

  • Vishnu Singh & Shiv Prasad Yadav & Sujeet Kumar Singh, 2021. "Duality theory in Atanassov’s intuitionistic fuzzy mathematical programming problems: Optimistic, pessimistic and mixed approaches," Annals of Operations Research, Springer, vol. 296(1), pages 667-706, January.
    • Handle: RePEc:spr:annopr:v:296:y:2021:i:1:d:10.1007_s10479-019-03229-8
    DOI: 10.1007/s10479-019-03229-8
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    References listed on IDEAS

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    3. Luhandjula, M.K. & Rangoaga, M.J., 2014. "An approach for solving a fuzzy multiobjective programming problem," European Journal of Operational Research, Elsevier, vol. 232(2), pages 249-255.
    4. A. Aggarwal & D. Dubey & S. Chandra & A. Mehra, 2012. "Application of Atanassov’s I-fuzzy set theory to matrix games with fuzzy goals and fuzzy payoffs," Fuzzy Information and Engineering, Springer, vol. 4(4), pages 401-414, December.
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