Stability of multiobjective nonlinear programming problems with random variables in the objective functions
type: Item
instance of: scholarly article
title: Stability of multiobjective nonlinear programming problems with random variables in the objective functions
zbMATH Open document ID: 0946.90551
DOI: 10.1016/S0165-0114(97)00130-9
author: Mohamed Abd El-Hady Kassem
published in: Fuzzy Sets and Systems
publication date: 2000-10-01T00:00:00Z
review text: 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.
reviewed by: S. Nickel
Mathematics Subject Classification ID: 90C70
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C31
zbMATH DE Number: 1339532
zbMATH Keywords: multiobjective nonlinear programming
zbMATH Keywords: random variables
zbMATH Keywords: stability
zbMATH Keywords: parametric programming
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1339532