Fuzzy rules extraction from support vector machines for multi-class classification

Abstract

This paper proposes a new method for fuzzy rule extraction from trained support vector machines (SVMs) for multi-class problems. SVMs have been applied to a wide variety of application. However, SVMs are considered "black box models", where no interpretation about the input-output mapping is provided. Some methods to reduce this limitation have already been proposed, however, they are restricted to binary classification problems and to the extraction of symbolic rules with intervals or functions in their antecedents. Hence, to improve the interpretability of the generated rules, this paper presents a new model for extracting fuzzy rules from a trained SVM. Moreover, the proposed model was developed for classification in multi-class problems. The generated fuzzy rules are presented in the format "IF x1 is C1 AND x2 is C1 AND ... AND xn is Cn, THEN x = (x1, x1, ⋯ xn) is of class A", where C1, C2, ..., Cn are fuzzy sets. The proposed method was evaluated in four benchmark databases (Bupa Liver Disorders, Wisconsin Breast Cancer, Iris and Wine). The results obtained demonstrate the capacity of the proposed method to generate a set of interpretable rules that explains the database and the influence of the input variables in the determination of the final class. © 2007 Springer-Verlag Berlin Heidelberg.