Data compression with homomorphism in covering information systems

In reality we are always faced with a large number of complex massive databases. In this work we introduce the notion of a homomorphism as a kind of tool to study data compression in covering information systems. The concepts of consistent functions related to covers are first defined. Then, by classical extension principle the concepts of covering mapping and inverse covering mapping are introduced and their properties are studied. Finally, the notions of homomorphisms of information systems based on covers are proposed, and it is proved that a complex massive covering information system can be compressed into a relatively small-scale information system and its attribute reduction is invariant under the condition of homomorphism, that is, attribute reductions in the original system and image system are equivalent to each other.