广义二型模糊逻辑系统质心降型及加权Karnik-Mendel算法

Centroid Type-reduction of General Type-2 Fuzzy Logic Systems and Weighted Karnik-Mendel Algorithms

随着广义二型模糊集的α-平面表达理论被提出,广义二型模糊逻辑系统在近年成为学术界热点研究问题。本文比较了离散Karnik-Mendel(KM)算法与连续版本的KM(continuous version of KM,CKM)算法中的运算,通过数值积分中牛顿-柯斯特求积公式把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算法在取特殊权重值下的一种例子。两个计算机仿真例子用来阐述和分析WKM算法的表现。总体来说,WKM算法在计算广义二型模糊逻辑系统质心解模糊化值时可取得比KM算法更小的绝对误差和更快的收敛速度,这给二型模糊逻辑系统的设计和应用提供了潜在的价值。

As the alpha-planes representation of general type-2 fuzzy sets(GT2 FSs) was proposed, general type-2 fuzzy logic systems(GT2 FLSs) have become a hot topic in academic field in recent years. The paper compares the Karnik-Mendel(KM) algorithms and the continuous version of KM(CKM) algorithms, extends the KM algorithms to three different forms of weighted KM(WKM) algorithms, whereas the KM algorithms just become a case of WKM algorithms as the weights of the latter are special. Three computer simulation examples are used to illustrate and analyze the performances of the WKM algorithms. On the whole, the WKM algorithms have smaller absolute error and faster convergence speed to calculate the centroid defuzzified value of GT2 FLSs compared with the KM algorithms, which provides the potential value for designing and applying T2 FLSs.