On properties of convex fuzzy mappings

The objective of this paper is to obtain some important properties about convex fuzzy mappings based on a linear ordering of fuzzy numbers proposed by Goetschel and Voxman. Firstly, a new kind of fuzzy mapping, termed semistrictly convex fuzzy mapping, is defined through this linear ordering. Note that semistrict convexity does not imply convexity. And the interrelationships among convex, strictly convex and semistrictly convex mappings are established under certain conditions. Furthermore, this paper obtains several characterizations for the above three classes of fuzzy mappings under the conditions of upper or lower semicontinuity. Finally, some further characteristic properties for semistrictly convex fuzzy mappings are derived.