Simplifying fuzzy rule-based models using orthogonal transformationmethods

摘要

An important issue in fuzzy-rule-based modeling is how to select anset of important fuzzy rules from a given rule base. Even though it isnconceivable that removal of redundant or less important fuzzy rules fromnthe rule base can result in a compact fuzzy model with betterngeneralizing ability, the decision as to which rules are redundant ornless important is not an easy exercise. In this paper, we introducenseveral orthogonal transformation-based methods that provide new ornalternative tools for rule selection. These methods include annorthogonal least squares (OLS) method, an eigenvalue decomposition (ED)nmethod, a singular value decomposition and QR with column pivotingn(SVD-QR) method, a total least squares (TLS) method, and a directnsingular value decomposition (D-SVD) method. A common attribute of thesenmethods is that they all work on a firing strength matrix and employnsome measure index to detect the rules that should be retained andneliminated. We show the performance of these methods by applying them tonsolving a nonlinear plant modeling problem. Our conclusions based onnanalysis and simulation can be used as a guideline for choosing a propernrule selection method for a specific application