2 research outputs found
A necessary and sufficient condition for two relations to induce the same definable set family
In Pawlak rough sets, the structure of the definable set families is simple
and clear, but in generalizing rough sets, the structure of the definable set
families is a bit more complex. There has been much research work focusing on
this topic. However, as a fundamental issue in relation based rough sets, under
what condition two relations induce the same definable set family has not been
discussed. In this paper, based on the concept of the closure of relations, we
present a necessary and sufficient condition for two relations to induce the
same definable set family.Comment: 13 page
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.Comment: 1