Development of Fuzzy Systems with Learning Capability

具有学习能力的模糊系统的开发

• 批准号: 10650393
• 负责人: ABE Shigeo
• 金额: $ 2.24万
• 依托单位: Kobe University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10650393/
• 关键词: Fuzzy Systems; Rule Acquisition; Pattern Recognition; Function Approximation; Neural Networks; Generalization Ability

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.

虽然神经网络的训练速度慢，训练后的网络的分析是困难的，他们有很高的泛化能力，为广泛的应用。相反，模糊系统很容易使用模糊规则进行分析，但它是难以获得的模糊规则和模糊系统的泛化能力不如神经网络。因此，我们的研究目标是开发具有更快的训练能力和更高的泛化能力的模糊系统。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。最初为每个类定义一个模糊规则。然后，如果识别率的分类是不够的，模糊规则的定义使用误分类的数据。该动态结构提高了分类器对离散输入数据的泛化能力。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，使得对基准数据的分类速度提高了2 ~ 7倍。当样本数小于输入变量数时，通过控制奇异值的大小来提高分类器的泛化能力。3.由于椭球区域模糊分类器是基于马氏距离的，4.通过扩展模糊分类器的椭球区域，建立了模糊函数逼近器，并对水的模糊分类器进行了验证净化厂

项目成果

S. Abe: "Fast Training of a Fuzzy Classifier with Pyramidal Membership Functions"SCI '99/ISAS '99. 3. 487-492 (1999)

S. Abe：“具有金字塔隶属函数的模糊分类器的快速训练”SCI 99/ISAS 99。

M.Shimizu and S.Abe: "On Input Invariance of Fuzzy Classifiers with Learning Capability"Transactions of ISCIE. 12(12). 739-746 (1999)

M.Shimizu 和 S.Abe：“具有学习能力的模糊分类器的输入不变性” ISCIE 汇刊。

N.Kasabov: "Neuro-Fuzzy Techniques for Intelligent Information Systems"Physica Verlag. 449 (1999)

N.Kasabov：“智能信息系统的神经模糊技术”Physica Verlag。

R.Thawonmas: "Function Approximation Based on Fuzzy Rules Extracted from Partitioned Numerical Data"IEEE Trans.Systems,Man,and Cybernetics-Part B. 29(4). 525-534 (1999)

R.Thawonmas：“基于从分区数值数据中提取的模糊规则的函数逼近”IEEE Trans.Systems、Man 和 Cyber​​netics - Part B. 29(4)。

S.Abe: "Fast Training of a Fuzzy Classifiere with Pyramidal Membership Functions"SCI'99/ISAS'99. 3. 487-492 (1999)

S.Abe：“具有金字塔隶属函数的模糊分类器的快速训练”SCI99/ISAS99。