Concave fuzzy set: a concept complementary to the convex fuzzy set

Abstract The concept of concave fuzzy set in Euclidean space is developed in this note. Useful properties of the concave fuzzy set are established. Some associated concepts like concave hull, concave containment and concavity tree are also defined and their computational approaches are described. The concepts can be used to decompose or approximate a fuzzy set. It may also be useful in the development of fuzzy geometry of space.