Dominance-based rough set theory over interval-valued information systems

This paper proposes a new generalization of classical real-valued information systems, that is, interval-valued information systems. By defining an interval-valued dominance relation on a condition attribute, a rough set model and attribute reduction are established over interval-valued information systems. Moreover, several interesting properties are investigated by constructive approach. Furthermore, knowledge reductions of consistent and inconsistent interval-valued dominance decision information systems are studied, respectively. Subsequently, some descriptive theorems of knowledge reduction are presented for interval-valued dominance decision information systems. Finally, the validity of the model and conclusions is verified by numerical example.