A Research On A Kind Of Upper And Lower Approximation Operator Defined On Covering Approximation Space And It’s Related Topology

The Rough set theory proposed by professor Pawlak in1982has been wildly studied around the world. Now the Rough set theory has been applied to many fields related with the real world successfully. In Rough set theory, upper and lower approximation operators are induced by an equivalence relation which is defined on domain of discourse. So the equivalence relation is a core concept-tion in Rough set theory.On the other hand, a partition can be determined by the equivalence relation which is defined on domain of discourse. So the upper and lower approximation operator can be given by a partition directly. A fact should arouse our attention—a partition is a cover and a cover is not generally a partition. Took this fact in-to consideration, the covering approximation space—It is a extension of Rough set theory—has been introduced after Zakowshi altered the partition into a cover. In this paper, a new kind of upper and lower approximation operator which is defined on covering approximation space is discussed as follow:Firstly, the background, current research situations, research methods, and applications about the covering approximation space are narrated.Secondly, the definition of a new upper and lower approximation operator in covering approximation space is given and some properties about it are discus-sed. Thirdly, comparing the new upper and lower approximation operator to the deeply studied ten upper and lower approximations operators, our main works are to find out the necessary and sufficient conditions for that the new upper and lower approximation operator and the every one of ten upper and lower approx-imations operators is identical respectively.Fourthly, in view of topology, the new upper and lower approximation opera-tor can be described by the interior and closed operator in a special topological space. The properties of this special topological space and some mapings which are defined on this kind of topological space are also investingated.Finally, the works of this paper are summarized and some expectations in future are proposed.