The widely used Support Vector Machine (SVM) method has shown to yield good results in Supervised Classification problems. When the interpretability is an important issue, then classification methods such as Classification and Regression Trees (CART) might be more attractive, since they are designed to detect the important predictor variables and, for each predictor variable, the critical values which are most relevant for classification. However, when interactions between variables strongly affect the class membership, CART may yield misleading information. Extending previous work of the authors, in this paper an SVM-based method is introduced. The numerical experiments reported show that our method is competitive against SVM and CART in terms of misclassification rates, and, at the same time, is able to detect critical values and variables interactions which are relevant for classification.