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Recently, in order to broad the application and theoretical areas of roughsets and matroids, some authors have combined them from many differentviewpoints, such as circuits, rank function, spanning sets and so on. In thispaper, we connect the second type of covering-based rough sets and matroidsfrom the view of closure operators. On one hand, we establish a closure systemthrough the fixed point family of the second type of covering lowerapproximation operator, and then construct a closure operator. For a coveringof a universe, the closure operator is a closure one of a matroid if and onlyif the reduct of the covering is a partition of the universe. On the otherhand, we investigate the sufficient and necessary condition that the secondtype of covering upper approximation operation is a closure one of a matroid.

Relationship between the second type of covering-based rough set and matroid via closure operator