Covering-Based Rough Sets on Eulerian Matroids

Abstract EN

Rough set theory is an efficient and essential tool for dealing with vagueness and granularity in information systems.

Covering-based rough set theory is proposed as a significant generalization of classical rough sets.

Matroid theory is a vital structure with high applicability and borrows extensively from linear algebra and graph theory.

In this paper, one type of covering-based approximations is studied from the viewpoint of Eulerian matroids.

First, we explore the circuits of an Eulerian matroid from the perspective of coverings.

Second, this type of covering-based approximations is represented by the circuits of Eulerian matroids.

Moreover, the conditions under which the covering-based upper approximation operator is the closure operator of a matroid are presented.

Finally, a matroidal structure of covering-based rough sets is constructed.

These results show many potential connections between covering-based rough sets and matroids.