Abstract:

The Rough set is studied using the medium set theory as a new tool. Firstly, some of its important properties of the standard medium operator are discussed; then the definition of medium operator with the corresponding equivalence relation is given, and it is shown that it satisfies the axiom. Considering the medium operator starting, the corresponding equivalence relations are constructed. Finally, it is proved that intermediary between the operator and equivalence are the only identified each other. The equivalence relations are transformed into a collection of Rough sets and the appropriate mediumiary operator will set into a medium set,which are equivalent. Rough set is brought into the framework of the medium theory axiom system, which lay a solid mathematical foundation for the Rough set.

Key words: Rough set; medium set theory; medium operator; equivalent relation