Covering Approximations in Set-Valued Information Systems

As one of three basic theories of granular computing, rough set theory provides a useful tool for dealing with the granularity in information systems. Covering-based rough set theory is a generalization of this theory for handling covering data, which frequently appear in set-valued information systems. In this paper, we propose a covering in terms of attribute sets in a set-valued information system and study its responding three types of covering approximations. Moreover, we show that the covering approximation operators induced by indiscernible neighborhoods and neighborhoods are equal to the approximation operators induced by the tolerance and similarity relations, respectively. Meanwhile, the covering approximation operators induced by complementary neighborhoods are equal to the approximation operators induced by the inverse of the similarity relation. Finally, by introducing the concept of relational matrices, the relationships of these approximation operators are equivalently represented.