Abstract: In our real life, there always arc a great deal of complex massive databases. The notion of homomorphism can be used as a tool to study data compression in consistented covering decision systems. First, we presented the concept of consistent function related to coverings, the concept of covering mapping, and their properties were studied. Next, we proposed the notion of homomorphism of consistent covering decision systems, and proved that a consistent covering decision system can be compressed into a relatively small-scale decision system. Meanwhile, their attribute reductions are equivalent to each other under the condition of homomorphism.

Key words: Consistent covering decision system, Consistent function, Covering mapping, Homomorphism, Data compression, Attribute reduction