A fuzzy classifier with ellipsoidal regions

Abstract

In this paper, we discuss a fuzzy classifier with ellipsoidal regions which has a learning capability. First, we divide the training data for each class into several clusters. Then, for each cluster, we define a fuzzy rule with an ellipsoidal region around a cluster center. Using the training data for each cluster, we calculate the center and the covariance matrix of the ellipsoidal region for the cluster. Then we tune the fuzzy rules, i.e., the slopes of the membership functions, successively until there is no improvement in the recognition rate of the training data. We evaluate our method using the Fisher iris data, numeral data of vehicle license plates, thyroid data, and blood cell data. The recognition rates (except for the thyroid data) of our classifier are comparable to the maximum recognition rates of the multilayered neural network classifier and the training times (except for the iris data) are two to three orders of magnitude shorter.