Enhanced Multivariable Fuzzy Modeling Supported by RBF Network

Abstract

The selection of optimum membership functions and deduction of rules from observed data can be implicitly carried out using conventional artificial neural networks, which can adaptively adjust membership functions and fine-tune rules to achieve better performance. This has resulted in many neuro-fuzzy approaches. These approaches, however do not contribute to the development of fuzzy logic. Also, selection of the number of processing nodes, the number of layers, and the interconnections among these layers in neural networks, still lacks systematic procedures. The purpose of this paper is to provide a systematic procedure for the construction of data driven fuzzy models, getting support from a special type multivariable function approximation network, known as radial basis functions (RBF) network the normalized form of which becomes equivalent to a fuzzy model. The normalized RBF network nodes in the hidden layer plays important role according to the case they are involved. One of the key features of normalized RBF networks is their excellent generalization. This property can be exploited to reduce the number of hidden nodes in function representation and classification tasks. To this end, normalized RBF network can be exploited to reduce the number of fuzzy sets in a fuzzy model while the explosive growth in multivariable case is greatly alleviated. The implication of this is the enhanced transparency and accuracy of the fuzzy model. These issues are investigated and the outcomes are reported in this research.