基于核映射的高阶Takagi-Sugeno模糊模型

本文研究规则后件为非线性函数的高阶Takagi-Sugeno(TS)模糊系统.为求解规则后件的函数表达式,首先通过一个核映射将原输入空间映射到高维特征空间,使原空间的非线性子模型转化为高维特征空间的线性子模型,获得了规则后件的非线性函数的计算公式.然后,给出了用核模糊聚类和最小二乘支持向量机设计模糊系统的一种新算法.最后通过4个公开数据集上的仿真实验验证了所提算法的逼近能力、推广能力和鲁棒性能.

Higher-order Takagi-Sugeno fuzzy model based on kernel mapping

This paper is concerned with higher-order Takagi-Sugeno(TS) fuzzy systems, where the consequent of a fuzzy rule is a nonlinear combination of input variables. To solve this problem, an implicit nonlinear kernel-mapping is introduced to map the original input space to some higher dimensional feature space, where locally nonlinear submodels of TS fuzzy systems are transformed into locally linear submodels; and then, the expressions of the consequent functions are presented. Furthermore, a novel algorithm of designing higher-order TS fuzzy systems is developed by combining the kernel-based fuzzy clustering with least squares support-vector-machines(LSSVM). Finally, the approximation accuracy, the generalization ability and robustness of the proposed algorithm have been demonstrated by simulation experiments on four well-known data sets.