Granulation based on hybrid information systems

In rough set theory, objects are partitioned into equivalence classes based on their attribute values, which are essentially functional information associated with the objects. Therefore, rough set theory can be viewed as a theory of functional granulation. In contrast, relational information systems (RIS) specify the relationships between objects, instead of the properties of objects. In this paper, we present a theory of granulation based on hybrid information systems (HIS), which combine functional information systems (FIS) and RIS. We study the relationship between FIS and RIS. We also define the indiscernibility relation based on relational information, and use it to develop a theory of granulation based on HIS.