Dynamic dominance rough set approach for processing composite ordered data

Abstract Dominance-based Rough Set Approach (DRSA) is a significant extended rough set model to process multi-criteria classification problems in which there needs to be consideration of the preference order between different objects. It can handle a special type of attributes with preference-ordered domains by a dominance relation. This article mainly focuses on employing the DRSA to process composite ordered decision systems including categorical, numerical, set-valued, interval-valued and missing attributes, and dynamic maintenance of the lower and upper approximations under the attribute generalization. Firstly, we introduce a new composite dominance-based rough set model in which the composite dominance relation may not satisfy three basic properties, i.e., reflexivity, symmetry and transitivity. Based on the proposed relation, we redefine the lower and upper approximations of upward and downward unions of decision classes. Then, we present matrix-based methods for calculating approximations through introducing the dominant (dominated) matrix and other induced matrices. In addition, we put forward the matrix-based incremental approaches for the update of approximations in composite ordered decision systems while the attribute set varies with time, which can avoid reconstructing these matrices from scratch. Finally, according to a series of comparative experimental results, it can easily be observed that our proposed incremental updating methods have a great advantage in improving the computational performance for dynamic attribute generalization.