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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Veröffentlicht in:	Fuzzy optimization and decision making Jg. 13; H. 2; S. 131 - 150
Hauptverfasser:	Gupta, S. K., Dangar, D.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Boston Springer US 01.06.2014 Springer Nature B.V
Schlagworte:	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
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Abstract	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.
AbstractList	(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) 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 ...-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.[PUBLICATION ABSTRACT] 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. (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).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 ...-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.
Author	Gupta, S. K. Dangar, D.
Author_xml	– sequence: 1 givenname: S. K. surname: Gupta fullname: Gupta, S. K. organization: Department of Mathematics, Indian Institute of Technology Roorkee – sequence: 2 givenname: D. surname: Dangar fullname: Dangar, D. email: debasisiitp@gmail.com organization: Department of Mathematics, Marwadi Education Foundation Group of Institutions
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Keywords	Duality results Mond-Weir dual Fuzzy number Hukuhara difference Fuzzy-valued function
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SubjectTerms	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
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Title	Duality for a class of fuzzy nonlinear optimization problem under generalized convexity
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