Ordering rules and complexity reduction for fuzzy models

The selection of a set of key fuzzy rules from a given rule base is an important issue for effective fuzzy modeling. For this purpose the clustering and orthogonal transformation methods are the essential tools. The determination of clusters representing fuzzy rules with the consideration of output as well as input spaces is essential. To select orthogonal axes as principal components other than those determined by Gram-Schmidt provides a most compact representation of the input space R^p with the p premise variables. This approach in principle possesses two important features for fuzzy modeling. On one hand an enhanced effective rule selection, with the consideration of consequence, is obtained. On the other hand substantial computational saving relative to conventional orthogonal-least-squares approach or other conventional clustering methods is achieved.