The discernibility approach for multi-granulation reduction of generalized neighborhood decision information systems

Attribute reduction of a decision information system (DIS) using multi-granulation rough sets is one of the important applications of granular computing. Constructing discernibility matrices by rough sets to get attribute reducts of a DIS is an important reduction method. By analyzing the commonalities between the multi-granulation reduction structure of decision multi-granulation spaces and that of incomplete DISs based on discernibility tool, this paper explored a general model for the multi-granulation reduction of DISs by the discernibility technique. First, the definition of the generalized neighborhood decision information system (GNDIS) was presented. Second, knowledge reduction of GNDISs by multi-granulation rough sets was discussed, and discernibility matrices and discernibility functions were constructed to characterize multi-granulation reduction structures of GNDISs. Third, the multi-granulation reduction structures of decision multi-granulation spaces and incomplete DISs were characterized by the reduction theory of GNDISs based on discernibility. Then, the multi-granulation reduction of GNDISs by the discernibility tool provided a theoretical foundation for designing algorithms of multi-granulation reduction of DISs.