Orthogonal transforms for ordering and reduction of fuzzy rules

We consider orthogonal transforms to order and select fuzzy rules. We show that, contrary to what has been stated in the literature, rank-revealing methods based on singular value decomposition do not produce an “importance ordering”. For systems modeling, when measured output data is available, the orthogonal least squares (OLS) method is more attractive. However, it does not fully respect rule redundancy, and this may hamper the generalization capabilities of the resulting model. As a rank-revealing rule ordering method, we advocate the use of a simple approach based on the pivoted QR decomposition only. Further, we show how detection of redundant rules can be introduced in the OLS algorithm. The methods are applied to a problem known from the literature and compared to results reported by other researchers