Development of Fuzzy Systems with Learning Capability

虽然神经网络的训练速度慢，训练后的网络分析困难，但它们具有很强的泛化能力，应用范围很广。相反，模糊系统很容易用模糊规则进行分析，但很难得到模糊规则，而且模糊系统的泛化能力弱于神经网络。因此，我们的研究目标是开发训练能力更强、泛化能力更强的模糊系统。主要研究成果如下：1.提出了一种椭球区域模糊分类器的动态训练结构。首先，为每一类定义一个模糊规则。然后，如果分类器的识别率不够，则使用错误分类的数据来定义模糊规则。通过这种动态结构，提高了分类器对离散输入数据集的泛化能力。2.通过对椭球区域模糊分类器进行Cholesky分解，并在计算隶属度函数时跳过近零元素，使基准数据的计算速度提高了2~7倍。当数据个数小于输入变量个数时，通过控制奇异值来提高泛化能力。3.由于椭球区域模糊分类器是基于马氏距离的，因此对输入变量的线性变换具有不变性。4.通过对椭球区域模糊分类器的扩展，构造了模糊函数逼近器，并将其应用于净水厂。

Although training of neural networks is slow and analysis of the trained networks is difficult, they have high generalization ability for a wide range of applications. On the contrary, fuzzy systems are easily analyzed using fuzzy rules but it is difficult to obtain fuzzy rules and generalization ability of fuzzy systems is inferior to that of neural networks. Thus our research target was to develop fuzzy systems with faster training capability and higher generalization ability. The research results are summarized as follows :1.Dynamic training architecture of a fuzzy classifier with ellipsoidal regions was developed. Initially for each class one fuzzy rule is defined. Then if the recognition rate of the classifier is not sufficient, fuzzy rules are defined using the misclassified data. By this dynamic architecture, the generalization ability of the classifier was improved for the data set with discrete inputs.2.By the Cholesky factorization and skipping the near zero elements in calculating the membership functions of the fuzzy classifier with ellipsoidal regions, two to seven times speed-up was obtained for the bench mark data. When the number of data is smaller than that of input variables, the generalization ability is improved by controlling the singular values.3.Since the fuzzy classifier with ellipsoidal regions is based on the Mahalanobis distance, it is shown to be invariant to linear transformation of input variables.4.Fuzzy function approximators were developed by extending the fuzzy classifier with ellipsoidal regions and their usefulness was demonstrated for the water purification plant.