关键词: 粗糙集, 相容关系, 最大相容类, 近似

Abstract: In Pawlak rough set model, the lower and upper approximations possess many mathematical properties, including the dual property. However, some of them may not hold in generalized rough set models. So, Yao defined new lower and upper approximations with respect to general binary relations based on right neighborhoods. In Yao’s definitions, the lower (upper) approximation was defined by the similar way with classical rough set, whereas the upper (lower) approximation was defined as the dual of the lower (upper) approximation. To preserve some properties in Pawlak’s model, this paper dually defines two types of lower and upper approximations based on the maximal tolerance classes in tolerance rough set model, and discusses their properties. Compared with the properties of the approximations defined in original tolerance rough set model, the new approximations proposed in this paper retain most of them, and satisfy some new properties.

Key words: rough set, tolerance relation, maximal tolerance class, approximation