基于加权Karnik-Mendel算法的区间二型模糊集质心计算

区间二型模糊集的质心计算(也称降型)在二型模糊逻辑系统中起着很重要的作用。Karnik-Mendel(KM)算法是完成降型的标准算法。本文介绍了区间二型模糊集相关理论,比较了离散KM算法与连续KM(continuous KM,CKM)算法中的运算,通过数值分析技术中牛顿-柯特斯求积公式将KM算法扩展成三种不同形式的加权KM(weighted KM,WKM)算法,而KM算法只是WKM算法的一种特例。计算机仿真例子用来阐述和分析WKM算法的表现,其在计算两种不对称区间二型模糊集质心时可取得比KM算法更小的绝对误差和更快的计算速度,这给二型模糊集及其模糊逻辑系统设计和应用提供了潜在的价值。

Weighted Karnik-Mendel Algorithms to Calculate the Centroids of Interval Type-2 Fuzzy Sets

Computing the centroids of interval type-2 fuzzy sets(it is also called the type-reduction)plays an important role in type-2 fuzzy logic systems.The paper introduces the corresponding theory of interval type-2 fuzzy sets and compares the operations in discrete Karnik-Mendel(KM)algorithms and continuous KM(CKM)algorithms.According to the Newton-Cote quadrature formulas of numerical integration techniques,the KM algorithms are extended to three different forms of weighted KM(WKM)algorithms,whereas the KM algorithms are only a special case of WKM algorithms.Computer simulation examples are given to illustrate and analyze the performances of WKM algorithms.While computing the centroids of two non-symmetric interval type-2 fuzzy sets,the WKM algorithms can obtain smaller absolute errors and faster computation speeds compared with the KM algorithms,which provides the potential value for designing and applying type-2 fuzzy sets and fuzzy logic systems.