K Granularity and Generalizd K Granularity Rough Set Model

The generalization of rough set is an important issue in rough set theory. In this paper, firstly, the concept of K-granularity rough relation is introduced, new models of K-granularity and generalized K-Granularity fuzzy rough sets are proposed based on the Dubois model, and then theirs structure are defined and properties proved. Secondly, some regularities of the changing of this model with the different granularity are discussed based on the attributes, and a method for measuring the uncertainty of the model is that monotonously increasing with the subdivision of granularity is proposed based on different granularity in this K-granularity fuzzy rough set. It can provide a theoretical basis for application of rough set in reality. Finally, an example is given to show the validity and effectiveness of K-granularity fuzzy rough set.