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

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.