Centroid of triangular and Gaussian type-2 fuzzy sets

In this paper, we present exact computation procedures for the centroid of type-2 fuzzy sets with either triangular or Gaussian secondary membership functions. We assume the standard formulation of the centroid based on the sup-min extension principle. The centroid of a triangular type-2 fuzzy set can be considered as a subsequent analytical extension of the KM type-reduction procedure dedicated to interval type-2 sets. The centroid of a Gaussian type-2 fuzzy set is recursively expressed by an independent procedure.