Identification of fuzzy models with the aid of evolutionary data granulation

The identification of fuzzy rule-based systems is considered. By their natu re, these fuzzy models are geared toward capturing relationships between in formation granules - fuzzy sets. The level of granularity of fuzzy sets hel ps establish a required level of detail that is of interest in the given mo delling environment. The form of the information granules themselves (in pa rticular their distribution and type of membership functions) becomes an im portant design feature of the fuzzy model, contributing to its structural a s well as parametric optimisation. This, in turn, calls for a comprehensive and efficient framework of information (data) granulation, and the one int roduced in the study involves a hard C-means (HCM) clustering method and ge netic algorithms (GAs). HCM produces an initial collection of information g ranules (clusters) that are afterwards refined in a parametric way with the aid of a genetic algorithm. The rules of the fuzzy model assume the form ' if x(1) is A and x(2) is B and ... and x(n) is W then y = phi (x(1), x(2),. ..,x(n), param) and come in two forms: a simplified one that involves concl usions that are fixed numeric values (that is, phi is a constant function), and a linear one where the conclusion part (phi) is viewed as a linear fun ction of inputs. The parameters of the rules are optimised through a standa rd method of linear regression (least square error method). An aggregate ob jective function with weighting factor used in this study helps maintain a balance between the performance of the model for training and testing data. The proposed identification framework is illustrated with the use of two r epresentative numerical examples.