Dependency space, closure system and rough set theory

This paper researches on potential relations of dependency space, closure system and rough set theory, and mainly focuses on solving some essential problems of rough set theory based on dependency space and closure system respectively. Firstly, we pretreat an information system into a relatively simple derivative system, in which dependency space and closure system are generated; Secondly, by means of dependency space and closure system separately we can solve some essential problems of rough set theory, such as reducts, cores; Finally, we reveal interior relations between dependency space and closure system. Conclusions of this paper not only help to understand rough set theory from the prospective of the dependency space and closure system, but also provide a new theoretical basis for data analysis and processing.