A New Support Vector Machine with Fuzzy Hyper-Plane and Its Application to Evaluate Credit Risk

Due to recent financial crises and regulatory concerns, financial intermediaries' credit risk assessment is an area of renewed interest in both the academic world and business community. Because in credit scoring areas we usually cannot label on customer as absolutely good who is sure to repay in time, or absolutely bad who will default certainly, in this paper, 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.