On the combination of rough set theory and grey theory based on grey lattice operations

Abstract

A new rough set named grey-rough set based on the grey lattice operation in grey system theory is proposed in this paper. Information systems records not only categorical data but also numerical data including a range of interval. In order to handle interval data in such information systems, we describe two sorts of new rough approximation after introduced grey lattice operations: a special grey-rough set based on the equivalence relation of interval coincidence, and a general grey-rough set based on the meet operation and the inclusion relation instead of the equivalence relation. The special grey-rough set is applicable to categorical data and numerical discrete data like the traditional rough set. The general grey-rough set is applicable to numerical interval data, which means that the proposal is an advanced method for non-deterministic information systems. The proposal is illustrated with several examples. © Springer-Verlag Berlin Heidelberg 2006.