Covering matroid
This work provides a theoretical extension in matroid theory and rough set theory, which could be useful for researchers in combinatorics and data analysis, but it appears incremental as it builds on existing concepts like partition matroids.
The paper introduces covering matroids as a new type of matroids that extend partition matroids by using coverings instead of partitions, and investigates their connections with covering-based rough sets and other special matroids like transversal matroids.
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 partition-circuit matroids. The relationships among several special matroids and covering matroids are studied.