Extended Graded Rough Sets Models Based On Covering

Rough sets theory, proposed by Pawlak in 1982, is an effective tool to deal with the fuzzy, uncertain, imprecise data. The classical rough set ignores the quantitative information of the class and the sets overlap, and the graded rough sets from the absolute quantification of infor-mation to expand the classic rough set. Rough sets based on partition, however, in real life, covering is more general than partition. In the covering approximation space, the graded rough sets is expanded from three aspects, which are the granularity, universe, and the combination of probabilistic rough sets.In the covering approximation space, integrating the idea of multi-granulation into graded rough sets, this study develops a multigranulation graded covering rough sets model. Basic properties of two types of multi-granulation graded covering rough sets model are investigated. Moreover, the relationships between the graded covering rough sets model and multi-granulation graded covering rough sets are explored. Finally, the practicability of the model is illustrated by an example.Through a combination of graded rough sets with covering rough sets over two different universes, this study develops a graded covering rough sets over two different universes. Firstly, upper and lower approximations are defined, improtant properties of the upper and lower ap-proximations are discussed. And then the model regions are defined and the properties of the model regions are disscussed. Moreover, the realationship between the covering variable preci-sion rough set model over two different universes and the present model is found.In the covering approximation space, based on the combination of probabilities rough sets and graded rough sets, this paper proposes a rough sets model regarding probabilities and grades based on covering. Firstly, the lower and upper approximations of the new model are constructed by two ways and basic properties of the lower and upper approximations of the new model are investigated. Moreover, the basic structure and accurate description of a rough sets regions are obtained. Finally, a practical example that adopts the new model in diagnostic systems is provided.