Elsevier

Fuzzy Sets and Systems

Volume 158, Issue 17, 1 September 2007, Pages 1873-1881
Fuzzy Sets and Systems

Optimal solutions in optimization problem with objective function depending on fuzzy parameters

https://doi.org/10.1016/j.fss.2007.04.003Get rights and content

Abstract

In this paper we first introduce a broad class of fuzzy optimization problems with an objective function depending on fuzzy parameters (FO problems) and introduce the concept α-maximal solutions of FO problems with respect to some fuzzy relation. We derive a simple and natural sufficient condition for a feasible solution to be an α-maximal solutions of FO problem. Later on we define possibly and necessarily α-maximal solutions of FO problems and prove that any possibly or necessarily α-maximal solution of FO problem is an α-maximal solution with respect to the possibilistic fuzzy relation or necessity fuzzy relation, respectively. The introduced concepts and results are illustrated and discussed on two numerical examples.

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