RETRACTED: Covering-based multigranulation decision-theoretic rough sets

In this paper, we study covering-based multigranulation decision-theoretic rough sets in a multi-covering space. From viewpoints of granule, we propose the notions of covering-based mean multigranulation decision-theoretic rough sets, covering-based optimistic multigranulation decision-theoretic ro ugh sets and covering-based pessimistic multigranulation decision-theoretic rough sets, realized, on the basis of Bayesian decision procedure. We first investigate some basic properties of those models. Then, we investigate the relationships between the proposed covering-based multigranulation decision-theoretic rough set models and other related rough set models. Thirdly, we elaborate on the interrelationships among the proposed models. Finally, an example is employed to illustrate the application of the proposed models.