The Robustness Of Fuzzy Classifiers

Support vector machine(SVM)and the resulting C-SVM,?-SVM andlearning of kernel function is the basic and most widely used theory and method in machine learning.For applications that contain uncertain information,such as in natural language processing,recommendation systems,and social network analysis,fuzzy classifiers are commonly used classification tools.Any classifier will work in a disturbing environment,and the sensitivity(robustness)of the classifier to the perturbation is important for the design of the classifier.In this paper,we study the robustness problem of the two classes of fuzzy classifier under the condition of non-box type perturbation.First,for a fuzzy SVM classifier determined by a class of product type decision functions,when the decision function constitutes a translational invariant kernel,it is proved that the classifier is robust under a kind of non-box type perturbation.The robustness of the corresponding positive definite fuzzy classifier(PDFC)is discussed.Then,A fuzzy ?-SVM classifier model with product decision function is proposed,and its equivalent form is given.Under certain conditions,it is proved that the classifier has robustness under non-box type perturbation,and the corresponding PDFC algorithm is given.The corresponding robustness problem is discussed.