A note on generalized convexity for fuzzy mappings through a linear ordering - 2013

In this paper, we study generalized convexity for fuzzy mappings that are defined through a linear ordering on the space of fuzzy intervals. On top of the concepts of convexity, preinvexity and prequasiinvexity, which have been introduced previously by other authors, we now introduce the concept of invex fuzzy mappings. For this purpose, we first consider the notion of strongly generalized differentiability for fuzzy mappings and we establish new properties thereof. Then, we introduce the ith strongly generalized partial derivative of a fuzzy function. After that, we present new characterizations for convex and invex fuzzy mappings. Finally, we study local-global minimum properties for convex and invex fuzzy mappings.