General type-2 fuzzy logic systems (GT2 FLSs) on the basis of alpha-plane representation of GT2 fuzzy sets (FSs) have attracted considerable attention in recent years. For the kernel type-reduction (TR) block of GT2 FLSs, the enhanced Karnik-Mendel (EKM) algorithm is the most popular approach. This paper proposes the sensible beginning divided-search EKM (SBDEKM) algorithms for completing the centroid TR of GT2 FLSs. Computer simulations are provided to show the performances of the SBDEKM algorithms. Compared with EKM algorithms and sensible beginning EKM (SBEKM) algorithms, the SBDEKM algorithms have almost the same accuracies and better computational efficiency.