The nature of statistical learning theory
The nature of statistical learning theory
Accurately learning from few examples with a polyhedral classifier
Computational Optimization and Applications
Fuzzy support vector machines based on spherical regions
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
Fuzzy support vector machines based on λ-cut
ICNC'05 Proceedings of the First international conference on Advances in Natural Computation - Volume Part I
A new fuzzy support vector machine to evaluate credit risk
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Neural Networks
Support Vector Machines with the Ramp Loss and the Hard Margin Loss
Operations Research
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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.