A fuzzy model of support vector classification algorithm

In this paper, we incorporate the concept of fuzzy set theory into the support vector machine (SVM) methodology. We apply a fuzzy membership to each input point and reformulate the optimization problem of SVM such that different input points can make different contributions to the learning of decision surface. Besides, the parameters to be identified in the SVM, such as the components within the weight vector and the bias term, are fuzzy numbers. This integration preserves the benefits of SVM learning theory and fuzzy set theory, where the SVM learning theory characterizes the properties of learning machines which enable them to effectively generalize the unseen data and the fuzzy set theory might be very useful for finding a fuzzy structure in an evaluation system.