In the present work, we introduce a new concept of harmonic convexity (concavity) under the fuzzy environment. The relations between the harmonic convex fuzzy mappings are explicitly discussed and many important results are obtained that relate the concept to fuzzy convexity and logarithmic convexity. Some properties are also obtained that relate the concept to fuzzy quasiconvexity.

fuzzy numbers, harmonic convex fuzzy mappings, quasiconvex fuzzy mappings.