Type-reduction (TR) is a key block for interval type-2 fuzzy logic systems (IT2 FLSs). In general, Karnik-Mendel (KM) (or enhanced Karnik-Mendel (EKM)) algorithms are used to perform the TR. These two types of algorithms have the advantage of preserving the uncertainties of membership functions (MFs) flow in IT2 FLSs. This paper gives the initialization explanations of KM and EKM algorithms, and proposes reasonable initialization enhanced Karnik-Mendel (RIEKM) algorithms for centroid TR of IT2 FLSs. By considering the accurate continuous Nie-Tan (CNT) algorithms as the benchmark, four computer simulation examples are adopted to illustrate and analyze the performances of RIEKM algorithms for solving the centroid TR and defuzzification of IT2 FLSs. Compared with the EKM algorithms, the proposed RIEKM algorithms have smaller absolute errors and faster convergence speeds, which afford the potential value for designing and applying IT2 FLSs.

中文翻译：

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区间2型模糊逻辑系统质心归约的合理初始化增强型Karnik-Mendel算法研究

减少类型（TR）是间隔2型模糊逻辑系统（IT2 FLS）的关键模块。通常，Karnik-Mendel（KM）（或增强的Karnik-Mendel（EKM））算法用于执行TR。这两类算法的优点是保留了IT2 FLS中隶属函数（MF）流的不确定性。本文给出了KM和EKM算法的初始化说明，并为IT2 FLS的质心TR提出了合理的初始化增强型Karnik-Mendel（RIEKM）算法。通过以精确的连续Nie-Tan（CNT）算法为基准，采用四个计算机仿真示例来说明和分析RIEKM算法解决IT2 FLS的质心TR和去模糊化的性能。与EKM算法相比，