Dynamic maintenance of approximations in set-valued ordered decision systems under the attribute generalization

Set-valued information systems are important type of data tables and generalized models of single-valued information systems. Approximations are the focal point of approaches to knowledge discovery based on rough set theory, which can be used to extract and represent the hidden knowledge in the form of decision rules. Attribute generalization refers to dynamic change of the attribute set in an information system with respect to the requirements of real-life applications. In this paper, we focus on maintaining approximations dynamically in set-valued ordered decision systems under the attribute generalization. Firstly, a matrix-based approach for computing approximations of upward and downward unions of decision classes is constructed by introducing the dominant and dominated matrices with respect to the dominance relation. Then, incremental approaches for updating approximations are proposed, which involves several modifications to relevant matrices without having to retrain from the start on all accumulated training data. Finally, comparative experiments on data sets from UCI as well as synthetic data sets show the proposed incremental updating methods are efficient and effective for dynamic attribute generalization.