基于加权Karnik-Mendel算法的区间二型模糊逻辑系统降型
Type-reduction of interval type–2 fuzzy logic systems with weighted Karnik-Mendel algorithms

二型模糊逻辑系统是当前的学术研究的热点问题, 而降型是该系统中非常重要的一个模块. Karnik-Mendel (KM)算法是被用来计算和完成区间二型模糊逻辑系统降型的标准算法. 通过比较离散版本KM算法中求和运算和 连续版本的KM(continuous version of KM, CKM)算法中求积分运算, 本文利用数值积分技术中牛顿- 柯斯特求积公 式将标准KM算法扩展成3种不同形式的加权KM(weighted KM, WKM)算法. 而KM算法只是WKM算法中的一种特 殊情况. 3个计算机仿真例子用来阐述和分析WKM算法的表现, 与传统的KM算法相比, WKM算法有较小的绝对误 差和较快的收敛速度, 给二型模糊逻辑系统设计者和应用者提供了潜在的应用价值.
Studies on type–2 fuzzy logic systems is a hot topic in the current academic area. While type-reduction is one of the most important blocks in the systems. KM algorithms are standarded algorithms which are used to compute and perform the type-reduction of interval type–2 fuzzy logic systems. By comparing the sum operation in discretized version KM algorithms and the integral operation in continuous version of KM (CKM) algorithms, the paper extends the standarded KM algorithms to three different forms of weighted KM (WKM) algorithms according to the Newton- Cotes quadrature formulas of numerical integration techniques. And the KM algorithms become a special case of the WKM algorithms. Three computer simulation examples are used to illustrate and analyze the performance of the WKM algorithms. Compared with the traditional KM algorithms, the WKM algorithms have smaller absolute error and faster convergence speed, which provide the potential application value for designers and adopters of type–2 fuzzy logic systems.