This paper presents a new model of support vector machines (SVMs) that handle data with tolerance and uncertainty. The constraints of the SVM are converted to fuzzy inequality. Giving more relaxation to the constraints allows us to consider an importance degree for each training samples in the constraints of the SVM. The new method is called relaxed constraints support vector machines (RSVMs). Also, the fuzzy SVM model is improved with more relaxed constraints. The new model is called fuzzy RSVM. With this method, we are able to consider importance degree for training samples both in the cost function and constraints of the SVM, simultaneously. In addition, we extend our method to solve one-class classification problems. The effectiveness of the proposed method is demonstrated on artificial and real-life data sets.

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