Hierarchical collapsing method for direct defuzzification of general type-2 fuzzy sets

Karnik-Mendel (KM) and Enhanced KM (EKM) algorithms are proved to be efficient approaches when dealing with general type-2 fuzzy sets represented by their α-planes. On the other hand, collapsing method, as a type-reduction algorithm for interval type-2 fuzzy sets has shown to be an effectual type-reduction method for interval type-2 fuzzy sets. In this paper, we aim at developing mathematical formulations based on collapsing procedure and α-plane decomposition in order to utilize geometric properties of general type-2 fuzzy sets for preparing a direct defuzzification procedure. The proposed methods are fast and robust. Extensive simulations have shown that the proposed algorithm outperforms most of the existing approaches in this field and its results are closer to the exact optimal defuzzified values.