Attributes set reduction in multigranulation approximation space of a multi-source decision information system

The multiple granular structures in multigranulation approximation space can be integrated by different approximation operators. These operators are induced by multigranulation rough set or others. In this paper, numerical algorithms of attributes set reduction are developed by using evidence theory or minimal elements of discernibility matrix, respectively. Firstly, a pair of multi-source rough approximation operators and their corresponding multigranulation rough approximation operators are defined based on a bijective and new transitional domain. Then, we propose attributes set reduction with respect to multi-source rough approximation. It is based on the relationship between multi-source rough approximations and evidence theory. Therefore, a heuristic algorithm of attributes set reduction for multi-source lower rough approximation is given. Secondly, we define a multigranulation variable precision rough set (MVRS) by considering weight of each attributes set relative to all of attributes sets. Finally, we investigate attributes set reduction with MVRS by combing the minimal elements of discernibility matrix and distribution discernibility function. There are some illustrative examples to elaborate the operation mechanism of above conclusions.