Concavoconvex fuzzy set

Abstract The concept of a concavoconvex fuzzy set in Euclidean space is reported. The idea is conceived by combining the concepts of convex and concave fuzzy sets together. Useful properties of the concavoconvex fuzzy set are established. The union/intersection of two concavoconvex fuzzy sets is either concavoconvex or concave/convex depending on the type of their characteristic function.