Evaluating Membership Functions for Fuzzy Discrete SVM

Abstract

A vast majority of classification problems are characterized by an intrinsic vagueness in the knowledge of the class label associated to each example. In this paper we propose a classifier based on fuzzy discrete support vector machines, that takes as input a binary classification problem together with a membership value for each example, and derives an optimal separation rule by solving a mixed-integer optimization problem. We consider different methods for computing the membership function: some are based on a metric defined in the attribute space; some derive the membership function from a scoring generated by a probabilistic classifier; others make use of frequency voting by an ensemble classifier. To evaluate the overall accuracy of the fuzzy discrete SVM, and to investigate the effect of the alternative membership functions, computational tests have been performed on benchmark datasets. They show that fuzzy discrete SVM is an accurate classification method capable to generate robust rules and to smooth out the effect of outliers.