A fuzzy multiple objective nonlinear optimization problem and its duality results

S. K. Gupta; D. Dangar; I. Ahmad; S. Al-Homidan

doi:10.3233/JIFS-171797

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 journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	1361-1373
Number of pages	13
Journal	Journal of Intelligent and Fuzzy Systems
Volume	36
Issue number	2
DOIs	https://doi.org/10.3233/JIFS-171797
State	Published - 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

Keywords

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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10.3233/JIFS-171797

Cite this

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AU - Dangar, D.

AU - Ahmad, I.

AU - Al-Homidan, S.

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PY - 2019

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AB - 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.

KW - Fuzzy valued function

KW - Hukuhara difference

KW - Mond-Weir type duality

KW - Multiple objective programming

KW - Partial ordering

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A fuzzy multiple objective nonlinear optimization problem and its duality results

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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