A Novel Approach to Building a Robust Fuzzy Rough Classifier

Currently, most robust classifiers with parameters focus on the determination of the optimal or suboptimal parameters. There are no research studies or even discussions about robust classifiers on all of the possible parameters. This paper considers the robust rough classifier and finds that the robust rough classifier satisfies a nested topological structure; then, the nested classifier, which reflects the classifier on all of the possible parameters, is proposed. First, some notions, such as the robust discernibility vector, the robust value reduct, and the robust covering vector, are proposed; these notions can reflect the classical corresponding notions on all of the possible parameters. It is more important that these notions share a common characteristic: the nested structure. The nested structure of these notions makes nested classifier theoretically possible. Furthermore, some novel algorithms are designed to compute the robust value reduct, the robust covering degree, and the robust classifier. These algorithms make the nested classifier technologically possible. Finally, numerical experiments demonstrate that the nested classifier is effective and efficient for classification and predication.