Discrete Non-iterative Centroid Type-Reduction Algorithms on General Type-2 Fuzzy Logic Systems

Abstract

Since the alpha-planes expressions of general type-2 fuzzy sets (GT2 FSs) have been proposed, general type-2 fuzzy logic systems (GT2 FLSs) that are dependent on GT2 FSs are becoming quite popular to fuzzy logic researchers. Usually enhanced Karnik–Mendel (EKM) algorithms are adopted for performing the kernel block of type-reduction (TR). However, the essence of EKM-based TR process probably hinders the GT2 FLSs from real-world applications. It is an intriguing as well as unsolved problem for comparing EKM algorithms with other non-iterative algorithms. This paper provides a framework encompassing fuzzy reasoning, defuzzification, as well as type-reduction. Furthermore, the continuous of NT (CNT) algorithm is shown to be a precise approach when it is used to execute the centroid TR of GT2 fuzzy logic systems. Four computer tests display the characteristics of discrete Nagar-Bardini (NB) and Nie-Tan (NT) non-iterative algorithms. Compared with EKM approach, the developed one exhibits some superiorities in terms of guaranteeing high computation accuracy and low computation burdens, which broadens the application ranges for the proposed method.