A Novel Method for Determining the Centroid of Type-3 Fuzzy Sets

Abstract Finding the centroid of a fuzzy set is one of the most crucial and significant computational tasks in fuzzy logic systems. Since Zadeh's time, centroids of type-1 and type-2 fuzzy sets have only been used in type-reduction. Although there are some applications for type-3 fuzzy control, there is currently no literature on the usage of centroid during type-reduction. The existing literature currently lacks a method for determining the centroid of the type-3 fuzzy set. In this study, we have attempted a relatively straightforward but rigorous way to find the centroid of a type-3 fuzzy set using weights in each direction of membership variables. This method may also be used to type-2 and type-1 fuzzy sets. Examples are provided that compare the computational results and show the computational efficiency of the proposed method.