Abstract: In classical multi-granulation rough set models,multiple equivalent relations (multiple granular structures) are used to approximate a target set.According to optimistic and pessimistic strategies,there are two types of common multi-granulation called optimistic multi-granulation and pessimistic multi-granulation respectively.The two combination rules seem to lack of practicability since one is too restrictive and the other too relaxed.In addition,multi-granulation rough set model is highly time-consuming because it is necessary to scan all the objects when approximating a concept.To overcome this disadvantage and enlarge the using range of multi-granulation rough set model,this paper firstly introduced the adjustable multi-granulation rough set model in incomplete information system and defined the local adjustable multi-granulation rough set model.Secondly,this paper proved that local adjustable multi-granulation rough set and adjustable multi-granulation rough set have the same upper and lower approximations.By defining the concepts of lower approximation cosistent set,lower approximation reduction,lower approximation quality,lower approximation quality reduction,and importance of internal and external,a local adjustable multi-granulation rough set model for attribute reduction was proposed.Furthermore,a heuristic algorithm of attribute reduction was constructed based on granular significance.Finally,the effectiveness of the method was illustrated through examples.The experimental results show that local adjustable size rough set model can accurately process the data of incomplete information system,and it can reduce the complexity of the algorithm.

Key words: Approximate quality, Attribute reduction, Incomplete information system, Multi-granulation, Rough set