关键词: 程度粗糙集, 双论域, 直觉模糊集, 优势关系, 模糊熵

Abstract: For the classical rough intuitionistic fuzzy set theory, only the minimum/maximum of membership and non-membership degree of the set are considered, while the membership and non-membership degree between the minimum and maximum of the set are neglected. Therefore, this problem is analyzed from the perspective of graded rough set in this paper. Firstly, graded rough set is introduced into the classical rough intuitionistic fuzzy set model, [μ(y)] and [ν(y)] are defined compared with the membership and non-membership degree between the minimum and maximum of the set. Then, the new lower and upper approximations are constructed. And four models are proposed. They are Type-I, Type-II graded rough intuitionistic fuzzy set models based on dominance relation and Type-I, Type-II two-universe graded rough intuitionistic fuzzy set models based on dominance relation. The related properties of these models are also discussed. Moreover, the boundaries of these models are narrowed. The value of fuzzy entropy is also reduced. Finally, the validity of these models is verified by examples.

Key words: graded rough set, two universes, intuitionistic fuzzy set, dominance relation, fuzzy entropy