Study on Sampling Based Discrete Nie-Tan Algorithms for Computing the Centroids of General Type-2 Fuzzy Sets

General type-2 fuzzy logic systems (GT2 FLSs) have become a hot topic in current academic field. Computing the centroids of general type-2 fuzzy sets (also called type-reduction) is a central block in GT2 FLSs. Recent studies prove the continuous Nie-Tan (CNT) algorithms to be actually an accurate approach to calculate the centroids of interval type-2 fuzzy sets (IT2 FSs). This paper compares the sum operation in discrete NT algorithms and the integral operation in CNT algorithms. According to the alpha-planes representation theory of general type-2 fuzzy sets (GT2 FSs), both the discrete and continuous NT algorithms can be extended to compute the centroids of GT2 FSs. Four computer simulation experiments indicate that, when the centroid type-reduced sets and defuzzified values of GT2 FSs are solved, to properly increase the number of sampling points of primary variable can make the results of discrete NT algorithms exactly approach to the accurate benchmark CNT algorithms. Furthermore, the computation efficiency of sampling based discrete NT algorithms is much higher than the CNT algorithms.