The Study And Application Of Fuzzy System Based On Feature Selection Clustering Method

With the rapid development of science and industrial production, various types of systems formed in today’s society and became more and more complex. When classic control theories are adopted to the analyses of these systems, problems such as nonlinearity and uncertainty will occur, which can affect the system function directly and enhance the difficulty coefficient and complexity of the system control. In addition, some control objects can not establish precise model in the process of actual control. At this moment, classical methods are difficult to play a role. Experts and scholars in this field are also seeking the theory and method solving this kind of system.The fuzzy model is an effective tool for uncertain nonlinear system approximation and has been applied successfully to control theory and techniques. TSK fuzzy systems provide a reasonable framework to model by decomposition of a nonlinear system into a collection of local linear models. Because traditional mathematical models may fail to describe the behaviors of many complex nonlinear systems, the potential application of TSK fuzzy models, therefore, is very broad. But the lack of interpretability in classic TSK fuzzy system consequent parameters loads reducing of fuzzy system interpretability. In addition, classic TSK fuzzy system has the problems that fuzzy rules are complex and redundant.Aiming at solving the problems in TSK fuzzy system, this paper carried out the following research:It is well known that the lack of interpretability of the classical TSK fuzzy system comes from that of the coefficients in the consequent polynomials. In this paper, we transform TSK fuzzy system to CTSK fuzzy system by centralization. The consequence coefficients of each rule in CTSK fuzzy system can be viewed as the corresponding first-order derivatives of its output at its rule center, and the consequence of each rule is equal to the Taylor’s first-order expansion of the output of the CTSK fuzzy system at the corresponding rule center, that is to say, CTSK fuzzy system has been highly interpreted in this way.Some sample features for establishing fuzzy system may be polluted by noise. It is not reasonable to generate fuzzy system using these features. This paper uses fuzzy clustering algorithm to determine fuzzy rules antecedent membership functions and simplify the sample features for reducing the complexity of fuzzy rules.After fuzzy rule antecedents have been determined, the estimation of consequent parameters can be viewed as a linear regression problem in the product space of the given input-output data. This paper casts the fuzzy system identification into a block sparse representation problem. In order to reducing the number of fuzzy rules and redundancy of rules, we extend orthogonal matching pursuit algorithm to block orthogonal matching pursuit algorithm for selecting important fuzzy rules.At last, this paper introduces feature selection and rules reduction into CTSK fuzzy system and proposes FCA-sparseCTSK algorithm. As a result, the fuzzy system becomes more interpretable and simplifies both the fuzzy rules and the number of fuzzy rules at the same time. The proposed FCA-sparseCTSK algorithm shows good performance in artificial datasets and real-world datasets.