Local Generalized Multigranulation Variable Precision Tolerance Rough Sets and its Attribute Reduction

In the era of big data, as for an important granular computing model, rough set model is an important tool for us to deal with data. As a kind of extension of classical rough sets, multigranulation rough sets have two forms, including optimistic and pessimistic cases. However, these two models have their shortcomings, one is too loose, and the other is too strict. To overcome the above shortcomings, based on the concept of local multigranulation tolerance rough sets in set-valued information systems, the local generalized multigranulation variable precision tolerance rough sets model by introducing characteristic function is established. Then the related properties are studied and proved. In addition, we define the concepts of lower approximate quality, inner and outer importance of attribute according to different granularity structures in set-valued decision information systems because different granularity structures have different effectives on the decision classes. Finally, the local attribute reduction algorithm and the global attribute reduction algorithm of local generalized multigranulation variable precision tolerance rough sets in set-valued decision information systems are given, and the effectiveness of the algorithms is proved by using UCI data sets.