On convex and concave fuzzy mappings

摘要

In this paper we introduce the concepts of convex subsets of 0, the set of all fuzzy numbers, and monotonic fuzzy mappings on R~2, and show that a monotonic fuzzy mapping F on a convex set C (is contained in) R~1 or R~2 is quasi-convex and quasi-concave. We establish two characterizations for convex fuzzy mappings, and two characterizations for concave fuzzy mappings. We also prove the least upper bound property.