Simplifying fuzzy rule-based models using orthogonal transformation methods

An important issue in fuzzy-rule-based modeling is how to select a set of i mportant fuzzy rules from a given rule base. Even though it is conceivable that removal of redundant or less important fuzzy rules from the rule base can result in a compact fuzzy model with better generalizing ability, the d ecision as to which rules are redundant or less important is not an easy ex ercise. In this paper, we introduce several orthogonal transformation-based methods that provide new or alternative tools for rule selection. These me thods include an orthogonal least squares (OLS) method, an eigenvalue decom position (ED) method, a singular value decomposition and QR with column piv oting (SVD-QR) method, a total least squares (TLS) method, and a direct sin gular value decomposition (D-SVD) method. A common attribute of these metho ds is that they all work on a firing strength matrix and employ some measur e index to detect the rules that should be retained and eliminated. We show the performance of these methods by applying them to solving a nonlinear p lant modeling problem. Our conclusions based on analysis and simulation can be used as a guideline for choosing a proper rule selection method for a s pecific application.