Definition of grey degree in set theory and construction of grey rough set models

The degree of uncertainty to which an object belongs to a class or not is viewed as grey degree,a formal approach to the definition of grey degree and levels of grey numbers are proposed in set theory.Then,grey rough set models are constructed,and some set theoretic properties of the proposed approach are discussed.Finally,an example is given to illustrate the proposed approach.The results show that the semantics of grey degree for the objects which can be classified properly are explicitly stated,and the levels of grey numbers can be reasonably interpreted.The grey rough set model can be applied to obtain the set of rules with different certainty degrees from inconsistent decision tables.