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.