Application of statistical information criteria for optimal fuzzy model construction

Theoretical studies have shown that fuzzy models are capable of approximating any continuous function on a compact domain to any degree of accuracy. However, constructing a good fuzzy model requires finding a good tradeoff between fitting the training data and keeping the model simple. A simpler model is not only easily understood, but also less likely to overfit the training data. Even though heuristic approaches to explore such a tradeoff for fuzzy modeling have been developed, few principled approaches exist in the literature due to the lack of a well-defined optimality criterion. In this paper, we propose several information theoretic optimality criteria for fuzzy models construction by extending three statistical information criteria: 1) the Akaike information criterion [AIC] (1974); 2) the Bhansali-Downham information criterion [BDIC] (1977); and 3) the information criterion of Schwarz (1978) and Rissanen (1978) [SRIC]. We then describe a principled approach to explore the fitness-complexity tradeoff using these optimality criteria together with a fuzzy model reduction technique based on the singular value decomposition (SVD). The role of these optimality criteria in fuzzy modeling is discussed and their practical applicability is illustrated using a nonlinear system modeling example.