Boolean matrix decomposition through covering-based rough sets

Boolean matrix decomposition has wide applications in role mining and data mining. Covering is a common form of data and covering-based rough sets provide an efficient tool to process this form of data. In this paper, we study boolean matrix decomposition from the viewpoint of covering-based rough sets. First, the covering approximation operators are concisely characterized by boolean matrices. Second, inspired by the matrix representation of the upper approximation operator, we present a sufficient and necessary condition for a square boolean matrix to decompose into the boolean product of another boolean matrix and its transpose. Finally, we present an algorithm for obtaining optimal boolean matrix decomposition since the decomposition is not unique.