Fuzzy Support Vector Machines for Pattern Classification

In conventional support vector machines (SVMs), an n-class problem is converted into n two-class problems. For the ith two-class problem we determine the optimal decision function which separates class i from the remaining classes. In classification, a datum is classified into class i only when the value of the ith decision function is positive. In this architecture, the datum is unclassifiable if the values of more than one decision function are positive or all the values are negative. In this paper, to overcome this problem, we propose fuzzy support vector machines (FSVMs). Using the decision functions obtained by training the SVM, for each class, we define a truncated polyhedral pyramidal membership function. Since, for the data in the classifiable regions, the classification results are the same for the two methods, the generalization ability of the FSVM is the same with or better than that of the SVM. We evaluate our method for three benchmark data sets and demonstrate the superiority of the FSVM over the SVM.