On the Combination of Rough Set Theory and Grey Theory Based on Grey Lattice Operations

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.

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