A neuro-fuzzy system modeling with self-constructing rule generation and hybrid SVD-based learning

We propose a novel approach for neuro-fuzzy system modeling. A neuro-fuzzy system for a given set of input-output data is obtained in two steps. First, the data set is partitioned automatically into a set of clusters based on input-similarity and output-similarity tests. Membership functions associated with each cluster are defined according to statistical means and variances of the data points included in the cluster. Then, a fuzzy IF-THEN rule is extracted from each cluster to form a fuzzy rule-base. Second, a fuzzy neural network is constructed accordingly and parameters are refined to increase the precision of the fuzzy rule-base. To decrease the size of the search space and to speed up the convergence, we develop a hybrid learning algorithm which combines a recursive singular value decomposition-based least squares estimator and the gradient descent method. The proposed approach has advantages of determining the number of rules automatically and matching membership functions closely with the real distribution of the training data points. Besides, it learns faster, consumes less memory, and produces lower approximation errors than other methods.