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Optimal solutions in optimization problem with objective function depending on fuzzy parameters
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DOI：10.1016/j.fss.2007.04.003.png)
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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 a-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 a-maximal solutions of FO problem. Later on we define possibly and necessarily a-maximal solutions of FO problems and prove that any possibly or necessarily a-maximal solution of FO problem is an a-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. (C) 2007 Elsevier B.V. All rights reserved.
Keyword:
fuzzy optimization
fuzzy objective function
fuzzy parameters
possibly and necessarily optimal solution
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