TL;DR
This paper introduces covering matroids, a new class extending partition matroids, and explores their relationships with covering-based rough sets and existing special matroids, enhancing combinatorial modeling in data analysis.
Contribution
It proposes covering matroids as an extension of partition matroids, linking them to covering-based rough sets and various special matroids, broadening theoretical understanding.
Findings
Covering matroids extend partition matroids.
Connections established between covering matroids and covering-based rough sets.
Relationships identified among covering matroids and other special matroids.
Abstract
In this paper, we propose a new type of matroids, namely covering matroids, and investigate the connections with the second type of covering-based rough sets and some existing special matroids. Firstly, as an extension of partitions, coverings are more natural combinatorial objects and can sometimes be more efficient to deal with problems in the real world. Through extending partitions to coverings, we propose a new type of matroids called covering matroids and prove them to be an extension of partition matroids. Secondly, since some researchers have successfully applied partition matroids to classical rough sets, we study the relationships between covering matroids and covering-based rough sets which are an extension of classical rough sets. Thirdly, in matroid theory, there are many special matroids, such as transversal matroids, partition matroids, 2-circuit matroid and…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsRough Sets and Fuzzy Logic · Data Mining Algorithms and Applications · Data Management and Algorithms