关键词: 近似空间, 复合, 粗糙集, 模糊集, 矩阵

Abstract: This paper mainly discusses the problem about calculating the upper and lower approximates of rough set in approximation space. Because a relation can be represented by a matrix and matrix operations are simple and intuitive, this paper proposes the calculation of the upper and lower approximates in rough set based on relation matrix and matrix operations. Firstly, this paper studies the compositions of two generalized approximation spaces and two generalized fuzzy approximation spaces, discusses the relationships between the operators in the composite approximation space and the two original approximation spaces, and shows that the generalized fuzzy approximation space is the further promotion of the generalized approximation space. Then, according to the matrix representation and the operation of the relation, this paper describes some operations and related properties in approximation space by matrix. Finally, this paper introduces the calculation of the upper and lower approximations of rough set in approximation space in matrix method. The theoretical proof shows that the matrix method is feasible and effective.

Key words: approximation space, composition, rough set, fuzzy set, matrix