Properties on inclusion relations and division charts in non-deterministic information systems

In rough set theory, the concept of the consistency is characterized by the inclusion relation of equivalence classes. This property connects rough sets with granular computing. In this paper, we consider properties on inclusion relations, and propose a diagram named a division chart. We examine several properties in five cases. This division chart shows us visual information about inclusion relations and the consistency. Furthermore, we clarify the previously proposed calculation methods by the division chart.