Rough set analysis of relational structures

In classical rough set theory, objects are partitioned into equivalence classes based on their attribute values, which essentially represent the functional information associated with the objects. Therefore, rough set theory can be viewed as a theory of functional granulation. In contrast, relational information systems (RISs) specify the relationships between objects, instead of their properties. This study presents a rough set analysis of relational structures, which are more general than functional information systems (FISs) and RISs. Unlike classical rough set theory, in which the attribute values of objects fully determine the indiscernibility relation, the rough set analysis of relational structures must account for the relationships between objects. This study considers three important concepts of indiscernibility with respect to relational structures: congruence, bisimulation, and exact equivalence. Using these indiscernibility relations, we investigate rough approximations and knowledge reduction. This study extends the application scope of rough set analysis from table-style information systems to relational structures. This extension is important because relational structures play a crucial role in the processing of complex data, such as graph mining or social network analysis.