Generalized multigranulation rough sets and optimal granularity selection

Multigranulation rough set theory is a desirable direction in the field of rough set, in which upper and lower approximations are approximated by multiple granular structures. However, classic multigranulation rough set is studied from two kinds of qualitative combination rules which were generated by pessimistic and optimistic viewpoints, respectively. The two combination rules seem to lack of practicability since one is too restrictive and the other too relaxed. To overcome this disadvantage, we propose a generalized multigranulation rough set model in this paper. First, we discuss upper and lower approximation sets of a generalized multigranulation rough set by introducing a support characteristic function and an information level. Then, as one of the most important problems in granular computing, we carefully study how to select optimal granularity in generalized multigranulation rough sets. Furthermore, algorithms of optimal granularity selection are constructed, by which we can provide an efficient approach to compute the optimal granularity based on generalized multigranulation rough sets. Finally, an illustrative example is given to show the effectiveness of the proposed approach. The main contribution of this paper is to construct the model of the optimal particle size selection on account of the generalized multi granularity, and overcome the limitation of the classical multi granularity.