Abstract: The target concept of multi-granulation rough sets is a kind of granular structure approximation induced by multiple binary relations, which is a valuable direction in the field of rough sets and has been widely used in practice. However, there are a lot of unlabeled data when the data set is large, and calculating the approximation of the target concept requires to calculate the equivalent class of all objects, which takes a lot of time to describe the approximation of the target concept as well as the complicated calculation process. Therefore, a local generalized multi-granulation rough set model is proposed. Firstly, the lower and upper approximations are defined by introducing characteristic functions. Secondly, a matrix method is proposed to solve the lower approximation and the upper approximation of the local generalized multi granularity rough set, and their properties are further studied. Finally, an example is given to verify the effectiveness of the proposed model, the algorithm to find the lower approximation of the local generalized multi granularity rough set is given. Besides, the model can make full use of the data information in the target concept to process data, which saves a lot of calculating time.

Key words: multi-granulation rough set, local rough set, characteristic function, matrix