Duality for a class of fuzzy nonlinear optimization problem under generalized convexity

In this paper, a Mond-Weir type dual program for a nonlinear primal problem under fuzzy environment is formulated. The solution concept of primal-dual problems is inspired by the nondominated solution. We have considered ordering among fuzzy numbers as a partial ordering and using the concept of Huk...

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Bibliographic Details
Published in:Fuzzy optimization and decision making Vol. 13; no. 2; pp. 131 - 150
Main Authors: Gupta, S. K., Dangar, D.
Format: Journal Article
Language:English
Published: Boston Springer US 01.06.2014
Springer Nature B.V
Subjects:
Artificial Intelligence
Calculus of Variations and Optimal Control; Optimization
Control algorithms
Decision making
Fuzzy
Fuzzy logic
Fuzzy set theory
Fuzzy sets
Fuzzy systems
Inventory control
Linear programming
Mathematical Logic and Foundations
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Nonlinear programming
Nonlinearity
Numbers
Operations Research/Decision Theory
Optimization
Order disorder
Probability Theory and Stochastic Processes
Set theory
Simplex method
Studies
Duality results
Mond-Weir dual
Fuzzy number
Hukuhara difference
Fuzzy-valued function
ISSN:1568-4539, 1573-2908
Online Access:Get full text
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Summary:In this paper, a Mond-Weir type dual program for a nonlinear primal problem under fuzzy environment is formulated. The solution concept of primal-dual problems is inspired by the nondominated solution. We have considered ordering among fuzzy numbers as a partial ordering and using the concept of Hukuhara difference between two fuzzy numbers and H -differentiability, appropriate duality theorems are established under pseudo/quasi-convexity assumptions. We have also illustrated a numerical example which satisfies the duality relations discussed in the paper.
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ISSN:1568-4539
1573-2908
DOI:10.1007/s10700-013-9176-7