Homomorphisms between relation information systems

Authors:
Changzhong Wang;Congxin Wu;Degang Chen
Affiliations:
Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, P.R.China;Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, P.R.China;School of Mathematics & Physics, North China Electric Power University, Beijing, P.R.China
Venue:
RSKT'07 Proceedings of the 2nd international conference on Rough sets and knowledge technology
Year:
2007

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Abstract

Information system is one of the important mathematical models in the field of artificial intelligence. The concept of homomorphism is very useful to study the communication between two information systems. In this paper, some properties of relation information systems under homomorphisms are investigated. The concept of a relation mapping between two universes is 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 mapping are studied. Furthermore, the notion of homomorphism of information systems based on arbitrary binary relations is proposed, and it is proved that the reductions of the original system and image system are equivalent to each other under the condition of homomorphism.