Abstract: The notion of homomorphism is used as a tool to deal with date compression in neighborhood information systems. We reviewed the notions of neighborhood information systems and the induced neighborhood information sys- terns. Then a novel definition of consistent function was proposed, and some important properties of neighborhood infor- mation systems under homomorphism were discussed. Furthermore, we proved that the reduction of the original system and its image system is equivalent to each other. I3y calculating the reduction of the less data image system, a more con- venient measure to handle the date compression of the original system was obtained.

Key words: Neighborhood information systems, Consistent function, Homomorphism, Reduction