Matroids and submodular functions for covering-based rough sets

Abstract

Covering-based rough set theory is an extension of Pawlak’s rough set theory, and it was proposed to expand the applications of the latter to more general contexts. In this case a covering is used instead of the partition obtained from an equivalence relation. Recently many authors have studied the relationships between covering-based rough sets, matroids and submodular functions. In this paper, we present the matroidal structures obtained from different partitions and coverings of a specific set. We also propose an extension of a matroidal structure for covering-based rough sets. Finally, we establish a partial order relation among the matroidal structures via submodular functions, coverings, and their approximation operators.