Communicating between information systems

Communication between information systems is a basic problem in granular computing. The concept of homomorphism is a useful mathematical tool to study the communication between two information systems. In this paper, some properties of information systems under homomorphisms are investigated. The concepts of consistent functions are first introduced and their properties are investigated. The concepts of relation mappings between two universes are then proposed in order to construct a binary relation on one universe according to the given binary relation on the other universe. The main properties of the mappings are studied. Finally, the notions of homomorphisms of information systems based on arbitrary binary relations are proposed, and it is proved that attribute reductions in the original system and image system are equivalent to each other under the condition of homomorphism.