Decision-theoretic rough set approaches to multi-covering approximation spaces based on fuzzy probability measure.

Three way decision model, as a new and meaningful decision making method, has attracted much attention and various results and applications have been reported. This paper investigates decision-theoretic rough set (DTRS) approach in the framework of multi-covering approximation spaces. By integrating fuzzy probability measure into Bayesian decision procedure, we define the notions of covering-based mean multigranulation decision-theoretic rough sets, covering-based optimistic multigranulation decision-theoretic rough sets, and covering-based pessimistic multigranulation decision-theoretic rough sets. We first investigate the basic properties of the three proposed models. Second, we elaborate on the relationship between the proposed models and those existing in literature, and discuss the interrelationships of the models. Finally, an illustrative example is employed to show the application of the proposed models.