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

Authors:
Jaroslav Ramík
Affiliations:
Department of Mathematical Methods in Economics, Faculty of Business Administration, Silesian University, Karviná, Czech Republic
Venue:
Fuzzy Sets and Systems
Year:
2007

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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 @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.