Preinvexity and Φ1-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.