Rough approximations based on soft binary relations and knowledge bases

This paper studies rough approximations based on soft binary relations. Firstly, two pairs of rough approximations based on soft binary relations are investigated, and their properties are determined. Secondly, rough sets with respect to some parameter and the set of parameters are introduced, and the fact that every rough set is a special case of E-rough sets where E is the set of parameters is demonstrated. Thirdly, rough soft sets induced by soft binary relations are proposed, and their lattice structures are given. Fourthly, two kinds of topologies induced by soft reflexive relations are investigated. Finally, the fact that there exists a one-to-one correspondence between the family of all knowledge bases and the family of all soft equivalence relations is proved, and soft characterizations of knowledge structures in knowledge bases are provided, which shows that we can study knowledge bases using soft set theory.