The Karush-Kuhn-Tucker optimality conditions for the optimization problem with fuzzy-valued objective function

The Karush-Kuhn-Tucker (KKT) conditions for an optimization problem with fuzzy-valued objective function are derived in this paper. A solution concept of this optimization problem is proposed by considering an ordering relation on the class of all fuzzy numbers. The solution concept proposed in this paper will follow from the similar solution concept, called non-dominated solution, in the multiobjective programming problem. In order to consider the differentiation of a fuzzy-valued function, we use the Hausdorff metric to define the distance between two fuzzy numbers and the Hukuhara difference to define the difference of two fuzzy numbers. Under these settings, the KKT optimality conditions are elicited naturally by introducing the Lagrange function multipliers.