Granulation multi-label decision tables and three-level granulation attribute reductions of multi-label decision tables

Multi-label data is an important data type in machine learning. The rough set theory has been successfully used to deal with various data. However, the application of rough set theory to multi-label data is still not perfect. In this paper, we investigate the attribute reduction of multi-label data. First, in order to explore the attribute reduction of a multilabel decision table, this paper constructs the granulation multi-label decision table of a multi-label decision table. Moreover, we divide the granulation multi-label decision function in the granulation multi-label decision table to three levels, that is, macroscopic level, mesoscopic level and microscopic level. Second, we give some new characterizations of the complementary decision reduction of a multi-label decision table by means of the three-level granulation multilabel decision functions. Third, we define the concept of a granulation attribute reduction of a multi-label decision table, and establish three-level granulation attribute reductions, that is, the macroscopic-level, the mesoscopic-level and the microscopic-level granulation attribute reduction. Furthermore, we show that a complementary decision reduction of a multi-label decision table can be seen as a macroscopic-level granulation attribute reduction and thus it can be interpreted as a positive region reduction. Finally, by several comparative analysis, the reasonability, feasibility and effectiveness of the granulation attribute reduction are demonstrated.