Ordered Information Systems and Graph Granulation

The concept of an Information System, as used in Rough Set theory, is extended to the case of a partially ordered universe equipped with a set of order preserving attributes. These information systems give rise to partitions of the universe where the set of equivalence classes is partially ordered. Such ordered partitions correspond to relations on the universe which are reflexive and transitive. This correspondence allows the definition of approximation operators for an ordered information system by using the concepts of opening and closing from mathematical morphology. A special case of partial orders are graphs and hypergraphs and these provide motivation for the need to consider approximations on partial orders.