Enhanced centroid-flow algorithm for general type-2 fuzzy sets

The Centroid Flow (CF) algorithm is a newly proposed approach for computing the centroid of a type-2 fuzzy set Ã, which normally can be obtained by taking the union of the centroids of all the α-planes of Ã. The CF algorithm utilizes the Karnik-Mendel (KM) or the Enhanced KM (EKM) algorithm only once at the α = 0 α-plane, and then lets its result “flows” stepwise to the α = 1 α-plane. The CF algorithm avoids applying the KM/EKM algorithms at every α-plane, and, therefore, significantly improves the computational efficiency. However, certain approximation errors of the CF algorithm will gradually accumulate as the algorithm “flows” upwards, and, in some cases, this can slightly bias the overall outcome. This paper introduces an Enhanced CF (ECF) algorithm that can reduce such accumulative errors by half, and, therefore, allows us to compute the centroid of à with much higher accuracy.