Nonconvex fuzzy mappings and the fuzzy pre-variational inequality

In this paper, we introduce the concepts of fuzzy pseudoconvex, fuzzy invex, fuzzy pseudoinvex and fuzzy preinvex mapping from Rn to the set of fuzzy numbers, and put forward the concepts of fuzzy extended directional differential, subgradient and subdifferential. Some properties are obtained for fuzzy pseudoconvex, fuzzy invex, fuzzy pseudoinvex and fuzzy preinvex mapping; relations are discussed between the fuzzy pre-variational inequality and the fuzzy vector optimization problem.