Homomorphisms between the covering information systems

The system of information is an important mathematical model in many fields, such as data mining, artificial intelligence, and machine learning. The relation or mapping is a popular method for exploring the communication between two systems of information. In this paper, we first introduce the concepts of the covering relation or mapping and the inverse covering relation or mapping between two covering systems of information and investigate their properties. Then, we proposed the view of homomorphism of covering systems of information which are based on covering relation. Moreover, we proved that attribute reductions in the image system and original system are equivalent to each other under the conditions of homomorphism given in this paper.