Computing the Centroid of a General Type-2 Fuzzy Set by Means of the Centroid-Flow Algorithm

Previous studies have shown that the centroid of a general type-2 fuzzy set (T2 FS) (A) over tilde can be obtained by taking the union of the centroids of all the alpha-planes (each raised to level alpha) of (A) over tilde. Karnik-Mendel (KM) or the enhanced KM (EKM) algorithms are used to compute the centroid of each alpha-plane. The iterative features in KM/EKM algorithms can be time-consuming, especially when the algorithms have to be repeated for many alpha-planes. This paper proposes a newmethod named centroid-flow (CF) algorithm to compute the centroid of (A) over tilde without having to apply KM/EKM algorithms for every alpha-plane. Extensive simulations have shown that the CF algorithm can reduce the computation time by 75%-80% and 50%-75%, compared with KM and EKM algorithms, respectively, and still maintains satisfactory computation accuracy for various T2 FSs when the primary variable x and alpha-plane are discretized finely enough.