Communication between information systems with covering based rough sets

Communication between information systems is considered as an important issue in granular computing. The concept of homomorphism is an effective mathematical tool to study information exchange between information systems. This paper provides a study on some basic properties of covering information systems and decision systems under homomorphisms. First, we define consistent functions related to coverings and covering mappings between two universes, and study their properties. Then, we introduce the notions of homomorphisms of covering information systems and point out that a homomorphism is a special covering mapping between information systems. Furthermore, we investigate some important properties of homomorphisms in covering information systems and decision systems. It is proved that some basic properties of original systems, such as set approximations, attribute reductions, can be reserved under the condition of homomorphisms in both covering information systems and covering decision systems.