Fuzzy Sets and Systems
On several definitions of the differential of a fuzzy mapping
Fuzzy Sets and Systems
Fuzzy Sets and Systems
On fuzzy convexity and parametric fuzzy optimization
Fuzzy Sets and Systems
Three kinds of generalized convexity
Journal of Optimization Theory and Applications
Convexity and local Lipschitz continuity of fuzzy-valued mappings
Fuzzy Sets and Systems
On convex and concave fuzzy mappings
Fuzzy Sets and Systems
Fuzzy Sets and Systems
A class of convex fuzzy mappings
Fuzzy Sets and Systems
Fuzzy Weirstrass theorem and convex fuzzy mappings
Computers & Mathematics with Applications
Convexity and semicontinuity of fuzzy mappings
Computers & Mathematics with Applications
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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.