Applications of repeat degree on coverings of neighborhoods

TL;DR

This paper explores the concept of repeat degree in covering-based rough sets, analyzing conditions for neighborhoods to form partitions, be reducts, and methods for calculating coverings, advancing theoretical understanding in this area.

Contribution

It introduces the application of repeat degree to analyze coverings of neighborhoods, including conditions for neighborhoods to be reducts and methods for their calculation.

Findings

Provided necessary and sufficient conditions for a subset to be a reduct.

Identified conditions under which two coverings induce the same relation.

Developed a method to calculate coverings based on repeat degree.

Abstract

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.