Summary: Based on the ordering of fuzzy numbers space proposed by R. Goetschel jun. and W. Voxman [Fuzzy Sets Syst. 18, 31–43 (1986; Zbl 0626.26014)], the differentiability of fuzzy mappings is discussed. For a fuzzy programming with non-constraint conditions defined on an \(n\)-dimensional space, optimality conditions are presented by using gradients. Furthermore, the necessity condition (Kuhn-Tucker condition) of an optimal solution for a constrained fuzzy programming is also obtained. At the same time, sufficient conditions for optimality of a convex fuzzy programming and a test example are given.