Applications of repeat degree on coverings of neighborhoods
  In covering based rough sets, the neighborhood of an element is the
intersection of all the covering blocks containing the element. All the
neighborhoods form a new covering called a covering of neighborhoods. In the
course of studying under what condition a covering of neighborhoods is a
partition, the concept of repeat degree is proposed, with the help of which the
issue is addressed. This paper studies further the application of repeat degree
on coverings of neighborhoods. First, we investigate under what condition a
covering of neighborhoods is the reduct of the covering inducing it. As a
preparation for addressing this issue, we give a necessary and sufficient
condition for a subset of a set family to be the reduct of the set family. Then
we study under what condition two coverings induce a same relation and a same
covering of neighborhoods. Finally, we give the method of calculating the
covering according to repeat degree.
