Study on conditions of neighborhoods forming a partition

A rough set is basically an approximation representation of the given data. The representation is expressed in two subsets defined on the data set: the upper and lower approximations. As well known, there are many different definitions about the two approximations. An open question regarding rough set is how to characterize the conditions for a neighborhood of a data item using the upper and lower approximations to form a partition of the universe U of the data. In this paper, we address this open question by defining two special operators, and there are some significant results about them.