Abstract
Covering of neighborhoods is an important concept in covering-based rough sets. There are many unsolved issues related to coverings of neighborhoods. The concept of repeat degree is proposed to study under what condition a covering of neighborhoods is a partition. It enables us to deal with many issues related to coverings of neighborhoods when coverings are incomplete. This paper applies repeat degree to solve some fundamental issues in coverings of neighborhoods. First, we investigate under what condition a covering of neighborhoods is equal to the reduct of the covering which induces the covering of neighborhoods. Then we study under what condition two coverings induce the same relation and the same covering of neighborhoods. Finally, we propose an approach to calculate coverings through repeat degree.
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