The Topological Properties of the Approximation Operators on A CCD Lattice

Rough sets, a tool for data mining, deal with the vagueness and granularity in information systems. Rough approximations on a complete completely distributive lattice(CCD lattice for short) and brings generalizations of rough sets into a unified framework are discussed in [3]. This paper is devoted to the discussion of the relationship between approximations and topologies on a CCD lattice. It is proved that the set of all upper approximations (or of lower approximations) with respect to a partition consists of a clopen topology; and conversely, a clopen topology which obey disjoint axiom can be induced by approximations. Furthermore, the axiomatic characterizations of upper and lower approximations are presented.