基于训练空间重构的多模块TSK模糊系统

利用重构训练样本空间的手段，提出一种多训练模块Takagi-Sugeno-Kang （TSK）模糊分类器H-TSK-FS.它具有良好的分类性能和较高的可解释性，可以解决现有层次模糊分类器中间层输出和模糊规则难以解释的难题.为了实现良好的分类性能，H-TSK-FS由多个优化零阶TSK模糊分类器组成.这些零阶TSK模糊分类器内部采用一种巧妙的训练方式.原始训练样本、上一层训练样本中的部分样本点以及所有已训练层中最逼近真实值的部分决策信息均被投影到当前层训练模块中，并构成其输入空间.通过这种训练方式，前层的训练结果对后层的训练起到引导和控制作用.这种随机选取样本点、在一定范围内随机选取训练特征的手段可以打开原始输入空间的流形结构，保证较好或相当的分类性能.另外，该研究主要针对少量样本点且训练特征数不是很大的数据集.在设计每个训练模块时采用极限学习机获取模糊规则后件参数.对于每个中间训练层，采用短规则表达知识.每条模糊规则则通过约束方式确定不固定的输入特征以及高斯隶属函数，目的是保证所选输入特征具有高可解释性.真实数据集和应用案例实验结果表明，H-TSK-FS具有良好的分类性能和高可解释性.

Multi-module TSK Fuzzy System Based on Training Space Reconstruction

A multi-training module Takagi-Sugeno-Kang (TSK) fuzzy classifier, H-TSK-FS, is proposed by means of reconstruction of training sample space. H-TSK-FS has good classification performance and high interpretability, which can solve the problems of existing hierarchical fuzzy classifiers such as the output and fuzzy rules of intermediate layer that are difficult to explain. In order to achieve enhanced classification performance, H-TSK-FS is composed of several optimized zero-order TSK fuzzy classifiers. These zero-order TSK fuzzy classifiers adopt an ingenious training method. The original training sample, part of the sample of the previous layer and part of the decision information that most approximates the real value in all the training layers are projected into the training module of the current layer and constitute its input space. In this way, the training results of the previous layers play a guiding and controlling role in the training of the current layer. This method of randomly selecting sample points and training features within a certain range can open up the manifold structure of the original input space and ensure better or equivalent classification performance. In addition, this study focuses on data sets with a small number of sample points and a small number of training features. In the design of each training unit, extreme learning machine is used to obtain the Then-part parameters of fuzzy rules. For each intermediate training layer, short rules are used to express knowledge. Each fuzzy rule determines the variable input features and Gaussian membership function by means of constraints, in order to ensure that the selected input features are highly interpretable. Experimental results of real datasets and application cases show that H-TSK-FS enhances classification performance and high interpretability.