Multigranulation double-quantitative decision-theoretic rough sets based on logical operations

As two important expanded quantification rough sets models, the multigranulation decision-theoretic rough sets mainly uses conditional probability to show relative quantitative information in multigranulation framework, and the graded multigranulation rough set is used to measure absolute quantitative information. However, they only consider the absolute quantitative (relative quantitative) information in granular structure, but do not consider the relative quantitative (absolute quantitative) information. It means that they cannot reflect a complete information. In order to overcome the defect, this paper proposes two pairs of multigranulation double-quantitative decision-theoretic rough sets models based on Bayesian decision and graded multigranulation rough sets, which essentially indicate the relative and absolute information quantification. After further studies to discuss decision rules and the inner relationship between these two models. Furthermore, we introduce an illustrative case to show the effectiveness and superiority of our proposed models, and the results show that our methods are effective for dealing with practical problems. Finally, we present some experiments based on UCI data sets showing the advantages of our proposed models in classification performance.