A dynamic approach for updating the lower approximation in adjustable multi-granulation rough sets

Granular computing ( GrC ) is one of the key issues in the field of information sciences. Research on the theory and algorithms of granular computing has very important practical significance in huge amounts of information. In multi-granulation rough set theory, two subsets are calculated to approximate the target concept, which are extremely time-consuming for large-scale data. In this paper, to address the issue above, we propose efficient algorithms for updating the lower approximation when a single object is added into or deleted from the target concept in an incomplete information system. Firstly, adjustable multi-granulation rough sets ( AMGRSs ) are introduced in an incomplete information system, and the related properties and theorems are explored. Secondly, it is proved that local- AMGRSs and AMGRSs are equivalent in an incomplete information system. Finally, dynamic algorithms for updating the lower approximation are proposed, and the efficiency of these algorithms is verified by an experiment.