A fuzzy multiple objective nonlinear optimization problem and its duality results

S. K. Gupta*, D. Dangar, I. Ahmad, S. Al-Homidan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this study, we propose a formulation of a Mond-Weir type dual program for a multiobjective nonlinear optimization problem under fuzzy environment. To deal with the multiobjectivity in the formulation, we consider the concept of weak Pareto optimal solution in the fuzzy sense. We use the Hukuhara metric/ difference to define the distance/difference between two fuzzy numbers. Further, we establish weak and strong duality theorems under fuzzy pseudo/quasi-convexity assumptions. Moreover, we also validate these duality relations using various numerical illustrations.

Original languageEnglish
Pages (from-to)1361-1373
Number of pages13
JournalJournal of Intelligent and Fuzzy Systems
Issue number2
StatePublished - 2019

Bibliographical note

Funding Information:
The authors sincerely thank the reviewers for the recommendation, valuable comments and the interesting suggestions which have considerably improved the presentation of the paper. This research is supported by the King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, under the Internal Project No. IN161058.

Publisher Copyright:
© 2019 - IOS Press and the authors. All rights reserved


  • Fuzzy valued function
  • Hukuhara difference
  • Mond-Weir type duality
  • Multiple objective programming
  • Partial ordering

ASJC Scopus subject areas

  • Statistics and Probability
  • Engineering (all)
  • Artificial Intelligence


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