广义粗糙Vague集的理论研究

Study on generalized rough vague sets

提出了广义粗糙Vague集概念,并分别从构造性方法和公理化方法对其进行了研究。在构造性方法中,由一个二元经典关系R出发,构造出广义粗糙Vague集上的一对一元对偶近似算子R,R,并对近似算子R,R的性质进行了讨论。在公理化方法中,定义了一对一元对偶近似算子L,H,并对对偶近似算子L,H的最小公理集进行了研究。由研究可以发现,构造性方法中的对偶近似算子R,R与公理化方法中的对偶近似算子L,H是等价的。

In this paper, the generalized rough vague set is introduced. Both constructive and axiomatic approaches are used to study on it. In the constructive approach, one starts from a binary crisp relation R and defines a pair of dual approximation operators ↓-R and ^-R in generalized rough vague sets. In addition, the properties of dual approximation operators ↓-R and ^-R are discussed, In the axiomatic approach, a pair of dual approximation operators L and H is given and the axioms that must be satisfied by L and H are studied. It is shown that both approximation operators ↓-R（^-R） and L（H） are equivalent.