Constructing optimal fuzzy models using statistical information criteria

Theoretical studies have shown that fuzzy models are capable of approximating any continuous function on a compact domain to any degree of accuracy. However, good performance in approximation does not necessarily assure good performance in prediction or control. A fuzzy model with a large number of fuzzy rules may have a low accuracy of estimation for the unknown parameters. This is especially true when only limited sample data are available in building the model. Further, such a model often encounters the risk of overfitting the data and thus has a poor ability of generalization. A trade-off is thus required in building a fuzzy model: on the one hand, the number of fuzzy rules must be sufficient to provide the discriminating capability required for the given application; on the other hand, the number of fuzzy rules must be "parsimonious" to guarantee a reasonable accuracy of parameter estimation and a good ability of generalizing to unknown patterns. In this paper we apply statistical information criteria for achieving such a trade-off. In particular, we combine these criteria with an SVD (singular value decomposition) based fuzzy rule selection method to choose the optimal number of fuzzy rules and construct the "best" fuzzy model. The role of these criteria in fuzzy modeling is discussed and their practical applicability is illustrated using a nonlinear system modeling example.