基于Nie-Tan算法的区间二型模糊集质心计算:改变主变量采样个数

Nie-Tan Algorithms to Calculate the Centroids of Interval Type-2 Fuzzy Sets: With Varying the Sampling of Primary Variables

计算区间二型模糊集的质心(也称降型)是区间二型模糊逻辑系统中的一个重要模块。Karnik-Mendel(KM)迭代算法通常被认为是计算区间二型模糊集质心的标准算法。尽管如此,KM算法涉及复杂的计算过程,不利于实时应用。在各种改进类算法中,非迭代的Nie-Tan(NT)算法可节省计算消耗。此外,连续版本NT(CNT,continuous version of NT)算法被证明是计算质心的准确算法。本文比较了离散版本NT算法中求和运算和连续版本NT算法中求积分运算,通过四个计算机仿真例子证实了当适度增加区间二型模糊集主变量采样个数时,NT算法的计算结果可以精确地逼近CNT算法。

Calculating the centroids of interval type-2 fuzzy sets(also called type-reduction) is an important block in interval type-2 fuzzy logic systems. Karnik-Mendel algorithms are usually considered as the standard algorithms to calculate the centroids of interval type-2 fuzzy sets. However, the Karnik-Mendel algorithms involve complicated computations, which may not suitable for real applications. In the enhanced types of algorithms, the noniterative Nie-Tan(NT) algorithms can save the computational cost. Furthermore, the continuous version of Nie-Tan(CNT) algorithms are proved to be an accurate method for computing the centroids.This paper compares the sum operations in discrete version of NT algorithms and the integral operations in CNT algorithms. Four computer simulation examples are provided to verify that the computation results of NT algorithms can accurately approximate the CNT algorithms as the number of sampling of primary variables of interval type-2 fuzzy sets are increased appropriately.