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

  • Vishnu SinghEmail author
  • Shiv Prasad Yadav
  • Sujeet Kumar Singh
S.I.: MOPGP 2017
  • 26 Downloads

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.

Keywords

Fuzzy sets IF linear programming Primal-dual problems Duality approach Duality gap 

Notes

Acknowledgements

The first author is thankful to the Ministry of Human Resource and Development(MHRD), Govt. of India, India for providing financial grant. The authors would like to thank the Editor-in-Chief and anonymous referees for various suggestions which have led to an improvement in both the quality and clarity of the paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Vishnu Singh
    • 1
    Email author
  • Shiv Prasad Yadav
    • 1
  • Sujeet Kumar Singh
    • 2
  1. 1.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia
  2. 2.The Logistics Institute-Asia Pacific, National University of SingaporeSingaporeSingapore

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