Duality in the fuzzy-parametric space for fuzzy-parametric nonlinear programming problem

The concepts of fuzziness and parametric analysis are of importance to treat uncertainty in mathematical model and may offer certain more viewpoints. The basic notions of the parametric study in nonlinear programming problem are presented by Osman (Aplikace matematiky 22(5):318–332, 1977 ; Aplikace...

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Published in:Opsearch Vol. 55; no. 3-4; pp. 662 - 676
Main Authors: Osman, M. S., Abd Elazeem, A. M., Elsisy, M. A., Rashwan, M. M.
Format: Journal Article
Language:English
Published: New Delhi Springer India 01.11.2018
Springer Nature B.V
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ISSN:0030-3887, 0975-0320
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Abstract The concepts of fuzziness and parametric analysis are of importance to treat uncertainty in mathematical model and may offer certain more viewpoints. The basic notions of the parametric study in nonlinear programming problem are presented by Osman (Aplikace matematiky 22(5):318–332, 1977 ; Aplikace matematiky 22(5):333–348, 1977 ). In general, a parametric programming problem is not easy to be solved. In addition, sometime, solving a parametric programming problem with parameters in the objective is easier than solving a parametric problem with parameters in the constraints and vice versa. Therefore, a parametric study in duality space is important to facilitate solving a parametric programming problem. The fuzzy nonlinear problem is interested area for research as one of the tools for treating uncertainty. The fuzzy nonlinear problem when parameters in the objective function or constrains or both is called the fuzzy parametric nonlinear problem. Therefore, dealing with fuzziness and duality parametric space is concerned. In this paper, a novelty introduction to the fuzzy basic notions of parametric programming problem are clarified, the relations between the concepts concerning duality in parametric spaces which introduced by Osman et al. (Int J Math Arch 6(12):161–165, 2016 ) and the fuzzy concepts are presented. We present and define the fuzzy parametric notions of the set of feasible parameters, the solvability set, and the stability sets of the first and second kind. These notions are not defined before. The theoretical relations and an illustration example are introduced.
AbstractList The concepts of fuzziness and parametric analysis are of importance to treat uncertainty in mathematical model and may offer certain more viewpoints. The basic notions of the parametric study in nonlinear programming problem are presented by Osman (Aplikace matematiky 22(5):318–332, 1977 ; Aplikace matematiky 22(5):333–348, 1977 ). In general, a parametric programming problem is not easy to be solved. In addition, sometime, solving a parametric programming problem with parameters in the objective is easier than solving a parametric problem with parameters in the constraints and vice versa. Therefore, a parametric study in duality space is important to facilitate solving a parametric programming problem. The fuzzy nonlinear problem is interested area for research as one of the tools for treating uncertainty. The fuzzy nonlinear problem when parameters in the objective function or constrains or both is called the fuzzy parametric nonlinear problem. Therefore, dealing with fuzziness and duality parametric space is concerned. In this paper, a novelty introduction to the fuzzy basic notions of parametric programming problem are clarified, the relations between the concepts concerning duality in parametric spaces which introduced by Osman et al. (Int J Math Arch 6(12):161–165, 2016 ) and the fuzzy concepts are presented. We present and define the fuzzy parametric notions of the set of feasible parameters, the solvability set, and the stability sets of the first and second kind. These notions are not defined before. The theoretical relations and an illustration example are introduced.
The concepts of fuzziness and parametric analysis are of importance to treat uncertainty in mathematical model and may offer certain more viewpoints. The basic notions of the parametric study in nonlinear programming problem are presented by Osman (Aplikace matematiky 22(5):318–332, 1977; Aplikace matematiky 22(5):333–348, 1977). In general, a parametric programming problem is not easy to be solved. In addition, sometime, solving a parametric programming problem with parameters in the objective is easier than solving a parametric problem with parameters in the constraints and vice versa. Therefore, a parametric study in duality space is important to facilitate solving a parametric programming problem. The fuzzy nonlinear problem is interested area for research as one of the tools for treating uncertainty. The fuzzy nonlinear problem when parameters in the objective function or constrains or both is called the fuzzy parametric nonlinear problem. Therefore, dealing with fuzziness and duality parametric space is concerned. In this paper, a novelty introduction to the fuzzy basic notions of parametric programming problem are clarified, the relations between the concepts concerning duality in parametric spaces which introduced by Osman et al. (Int J Math Arch 6(12):161–165, 2016) and the fuzzy concepts are presented. We present and define the fuzzy parametric notions of the set of feasible parameters, the solvability set, and the stability sets of the first and second kind. These notions are not defined before. The theoretical relations and an illustration example are introduced.
Author Osman, M. S.
Abd Elazeem, A. M.
Rashwan, M. M.
Elsisy, M. A.
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  organization: Faculty of Economics and Political Science, Cairo University
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Cites_doi 10.1016/j.jmsy.2014.02.008
10.1016/j.ejor.2009.05.019
10.1287/mnsc.17.4.B141
10.1016/j.eswa.2016.07.034
10.1016/j.ejor.2012.01.052
10.3233/IFS-151644
10.1016/j.cam.2008.03.011
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Keywords Nonlinear programming problem
Parametric
Duality
Fuzzy set
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Snippet The concepts of fuzziness and parametric analysis are of importance to treat uncertainty in mathematical model and may offer certain more viewpoints. The basic...
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BASIC (programming language)
Business and Management
Fuzzy sets
Management
Mathematics
Nonlinear programming
Operations research
Operations Research/Decision Theory
Parameter uncertainty
Parametric analysis
Theoretical Article
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Title Duality in the fuzzy-parametric space for fuzzy-parametric nonlinear programming problem
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