Generalized convex fuzzy mappings and fuzzy variational-like inequality

In this paper, we introduce the concepts of some generalized convex fuzzy mappings from R n to the set of fuzzy numbers. Under the condition of upper or lower semicontinuity, a new criterion be obtained for the existence of a fuzzy preinvex mapping: a fuzzy preinvex mapping can be achieved when the invex subset of R n satisfies certain conditions. The relations between generalized convex fuzzy mappings are discussed, and some properties are obtained that relate the concepts of fuzzy pseudoinvex and fuzzy prequasiinvex mapping, fuzzy invex and fuzzy preinvex mapping, fuzzy preinvex and fuzzy prequasiinvex mapping. We also discuss the relationship between the fuzzy variational-like inequality (the fuzzy weak variational-like inequality) and fuzzy optimization problems, and an application example of a fuzzy variational-like inequality: the fuzzy variational-like inequality representation of a fuzzy transportation equilibrium problem.