Enhanced Centroid-Flow Algorithm for Computing the Centroid of General Type-2 Fuzzy Sets
Daoyuan Zhai, Jerry M. Mendel · IEEE Transactions on Fuzzy Systems · 2012
Recently, a centroid-flow (CF) algorithm has been proposed to compute the centroid of a type-2 fuzzy set Ã. This algorithm utilizes the Karnik-Mendel (KM) or the enhanced KM (EKM) algorithm only at the α = 0 α-level of Ã̃ and then lets its result “flow” upward to the α = 1 α-level of Ã. It avoids having to apply the KM/EKM algorithms at every α-level, which significantly improves its computational efficiency; however, the CF algorithm approximation errors will gradually accumulate as the algorithm “flows” upward, and in some cases, this can cause the centroid of the α = 1 α-level of à to differ from its theoretical value. This paper introduces an improved version of the CF algorithm, which is called enhanced CF algorithm, that reduces such accumulative errors by half and, therefore, greatly improves the computational accuracy.