Identification of fuzzy systems by means of genetic optimization and data granulation

Abstract

In this study, we introduce a new category of fuzzy inference systems based on data (information) granulation and show their applications to the identification of complex and usually nonlinear systems. Information granules are treated as collections of objects (data, in particular) brought together by the criteria of proximity, similarity, or functionality. The formal framework of information granulation along with the information granules themselves become an important design feature of fuzzy models, which in essence are geared towards capturing relationship between information granules rather than plain numeric data. The key characteristics of experimental data being used in the construction of the fuzzy model are carefully reflected by fuzzy rules formed therein. Information granulation realized with the aid of Hard C-Means (HCM) clustering helps determine the initial values of the parameters of the fuzzy models. This in particular concerns such important components of the rules as the initial apexes of the membership functions standing in the premise part of the fuzzy rules and the initial values of the polynomial functions present in their consequence part. The initial values of the parameters are tuned effectively with the aid of the genetic algorithms (GAs) and the least square method (LSM). An aggregate objective function is constructed in order to strike a sound balance between the approximation and generalization capabilities of the fuzzy model. The model is evaluated with the use of numerical experimentation and contrasted with the quality of some conventional fuzzy models already encountered in the literature.