Characteristic matrix of covering and its application to Boolean matrix decomposition

Covering-based rough sets provide an efficient theory to deal with covering data which widely exist in practical applications. Boolean matrix decomposition has been widely applied to data mining and machine learning. In this paper, three types of existing covering approximation operators are represented by boolean matrices, and then they are used to decompose into boolean matrices. First, we define two types of characteristic matrices of a covering. Through these boolean characteristic matrices, three types of existing covering approximation operators are concisely equivalently represented. Second, these operators are applied to boolean matrix decomposition. We provide a sufficient and necessary condition for a square boolean matrix to decompose into the boolean product of another one and its transpose. Then we develop an algorithm for this boolean matrix decomposition. Finally, these three types of covering approximation operators are axiomatized using boolean matrices. In a word, this work presents an interesting view to investigate covering-based rough set theory and its application.