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Fuzzy Sets and Systems
Article . 1999 . Peer-reviewed
License: Elsevier TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 1999
Data sources: zbMATH Open
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Stability of multiobjective nonlinear programming problems with random variables in the objective functions

Authors: Kassem, Mohamed Abd El-Hady;

Stability of multiobjective nonlinear programming problems with random variables in the objective functions

Abstract

The paper deals with stability in multiobjective nonlinear programming. Considering some earlier works by Luhandjula and the same author, Kassem tried to expand the concepts for possibilistic stability analysis in multiobjective optimization. Unfortunately, there are a lot of nebulosities in this article. The author does not really apply the concept of a-possibility efficient solutions introduced by \textit{M. K. Luhandjula} (Definition 4 in the article, cf. Definition 5 in [ibid. 21, 135-145 (1987; Zbl 0621.90085)] for the case of multiobjective maximization). The terms efficiency or set of efficient solutions are not defined at all, and there are many indications that the author has a wrong perception of it, i.e. assuming the uniqueness of an efficient solution. On many occasions, \(\min F(x,t)\) is used as if it were a vector and not a set a vectors. Since the concepts of efficiency and a-possibility efficiency are central to all other stability concepts, it is hard to say more about the value of the paper.

Related Organizations
Keywords

random variables, Sensitivity, stability, parametric optimization, parametric programming, Fuzzy and other nonstochastic uncertainty mathematical programming, multiobjective nonlinear programming, stability, Multi-objective and goal programming

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
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