Centroid of a general type-2 fuzzy set computed by means of the centroid-flow algorithm

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