The Nested Structure in Fuzzy Rough Classifier

Currently most robust fuzzy rough classifiers with parameters focus on the robustness and less-sensitiveness to noise. No work studies or even discusses about the topological structure of robust fuzzy rough classifiers. This paper finds that the robust rough classifier satisfies a nested topological structure, and then NESTED CLASSIFIER, which reflects the classifier on different parameters, is proposed. First some notions, such as robust discernibility vector, robust value reduct and robust covering vector, are proposed which share the common characteristic: the nested structure. The nested structure of these notions makes the nested classifier theoretically possible. Furthermore, some novel algorithms are designed to compute robust value reduct, robust covering degree and robust classifier. These algorithms make the nested classifier technologically possible. Finally numerical experiments demonstrate that the nested classifier is more efficient than the existing ones.