Abstract: The generalized type-2 fuzzy logic system has become a hot academic research issue in recent years, and the reduced type is the core module of the system. Recent studies have proved that the continuous Nie-Tan (CNT) algorithm is an accurate method to calculate the centroid of the interval type-2 fuzzy set. This paper discovers the internal connection between the summation operation in the discrete Nie-Tan (NT) algorithm and the integration operation in the CNT algorithm, and adopts two types of algorithms to perform the centroid type-reduction of generalized type-2 fuzzy logic systems  based on the alpha-planes representation theory of general type-2 fuzzy sets. Three computer simulation experiments prove that, when the number of sampling points of the main variable is appropriately increased, the centroid reduced set and defuzzified value of the generalized type-2 fuzzy logic system calculated by the proposed discrete NT algorithm based on the main variable sampling can be accurately close to the benchmark CNT algorithm, and the computational efficiency of the sampling discrete NT algorithm is much higher than that of the CNT algorithm.

Key words: general type-2 fuzzy logic systems, centroid type-reduction, discrete Nie-Tan algorithms, sampling, calculation accuracy ,