Abstract:

In the research of the rough set theory by algebraic approaches, an important method is to define some basic operators in the set of the pairs 〈R（X ）,R（X） 〉 , and find the algebraic structure constructed by the pairs. The most famous algebraic structures are the regular double Stone algebra and  the Nelson algebra. The paper starts from the set of pairs  〈R（X）, -R（X）〉 , by defining an implication operator, proves that this rough set formed d by the pairs becomes an implication lattice. The relation between the regular double Stone algebra and the rough implication lattice is studied. The r esults can lay a foundation for rough logic and rough reasoning.

Key words: rough sets, rough set algebra, implication lattice, regular double Stone algebra