Based on the ordering of fuzzy numbers proposed by Goetschel and Voxman,the representations and some properties of strongly preinvex fuzzy-valued function are defined and obtained,several new concepts of strongly monotonicities fuzzy functions are introduced,the relationship among the strongly preinvex,strongly invex and mono-tonicities under some suitable and appropriate conditions is established and a necessary condition for strongly pseudoinvex functions is given.As an application,the conditions of local optimal solution and global optimal solution in the mathematical programming problem are discussed.