Fuzzy support vector machines for solving two-class problems

A support vector machine (SVM) was originally developed to solve two-class non-fuzzy problems. An SVM can act as a linear learning machine when handling data in a high dimensional feature space for non-linear separable and non-separable problems. A few methods have been proposed to solve two-class and multi-class classification problems by including fuzzy concepts. In this paper, we propose a new fuzzy support vector machine which improves the traditional SVM by adding fuzzy memberships to each training sample to indicate degree of membership of this sample to different classes. This fuzzy SVM is more complete and meaningful, and could generalize the traditional non-fuzzy SVM to a fuzzy one, i.e., the traditional non-fuzzy SVM is an extreme case of our fuzzy SVM when the degrees of membership of a sample to two different classes are the same.