  The main objective of this paper is to derive the optimality conditions for
one type of fuzzy optimization problems. At the beginning, we define a cone of
descent direction for fuzzy optimization, and prove that its intersection with
the cone of feasible directions at an optimal point is an empty set. Then, we
present first-order optimality conditions for fuzzy optimization problems.
Furthermore, we generalize the Gordan's theorem for fuzzy linear inequality
systems and utilize it to deduce the Fritz-John optimality condition for the
fuzzy optimization with inequality constraints. Finally, we apply the
optimality conditions established in this paper to a binary classification
problem for support vector machines with fuzzy data. In the meantime, numerical
examples are described to demonstrate the primary findings proposed in the
present paper.
