Design of weighted based divided-search enhanced Karnik–Mendel algorithms for type reduction of general type-2 fuzzy logic systems

General type-2 fuzzy logic systems (GT2 FLSs) based on the $$\alpha$$ -planes representation of general T2 fuzzy sets (FSs) have become more accessible to FL investigators in recent years. Type reduction (TR) is the most important block for GT2 FLSs. Here the weighted type-reduction algorithms based on the Newton and Cotes quadrature formulas of numerical methods of integration technique are first given, and the searching spaces are divided. Then a type of weighted divided search enhanced Karnik–Mendel (WDEKM) algorithms is shown to complete the centroid TR. In contrast to the WEKM algorithms, four simulation instances show that the WDEKM algorithms get lesser absolute errors and faster calculational speeds, which may offer the potentially application values for applying T2 FLSs.