Preinvexity and Phi1-convexity of fuzzy mappings through a linear ordering

The preinvexity, prequasiinvexity, "1-convexity, and "1-quasiconvexity of fuzzy mappings are defined based on a linear ordering on the set of fuzzy numbers. Characterizations for these fuzzy mappings are obtained. The local-global minimum properties of real-valued preinvex functions and "1-convex functions are extended to preinvex fuzzy mappings and "1-convex fuzzy mappings, respectively. It is also proved that every strict local minimizer of a prequasiinvex fuzzy mapping is a strict global minimizer, and that every strict local minimizer of a "1-quasiconvex fuzzy mapping is a strict global minimizer.