Granularity reduction method based on positive decision holding for multi-granulation decision-theoretic rough set

Multi-granulation decision-theoretic rough set (MG-DTRS) is a generalisation of the multi-granulation rough set (MGRS) model through integrating the related properties of MGRSs and decision-theoretic rough sets (DTRSs), and it can realise decision analysis and processing of information systems from multiple perspectives and multi-level. Taking the optimistic MG-DTRS and the pessimistic MG-DTRS model as an example, MG-DTRS model and its related properties were discussed according to the DTRSs which construct positive, boundary and negative regions on the basis of two thresholds given by experts. Especially, the positive decision and its properties in MG-DTRS model were analysed. At the same time, it was found and proved that the positive decision is monotonic with the change of granularity in MG-DTRS model. Further, the granular structure selection problem was investigated under the MG-DTRS model, the concept of -decision granularity importance was introduced and a granularity reduction algorithm based on the positive decision holding for MG-DTRS model was designed and constructed. Finally, an example was given to prove that the algorithm is effective, and it has a small time complexity.