Dual Universes Multi-Granulation Covering Rough Sets Model

The rough set of classical multi-granulation decision theory is in return for the equivalence relation on the universe. But in practical application, the equivalence relation is difficult to be realized because of the incompleteness of information system. In this paper, multi-granulation decision theory and the covering rough sets model is extended to the dual universes model, and the dual universes multi-granulation covering rough sets model is proposed. The minimal covering description is given, in addition, the definition of lower and upper approximation is constructed to deal with knowledge of multiple granularity space of distributed data. The practicability and reliability of this model are proved by introducing the uncertainty measurement of rough entropy and information entropy.