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

摘要： 针对经典粗糙直觉模糊集理论仅考虑了集合中的最小/最大隶属度与非隶属度，而忽略了介于二者之间的隶属度与非隶属度的问题，从程度粗糙集的角度对其进行了分析研究。首先，将程度粗糙集引入到经典粗糙直觉模糊集模型中，定义了[μ(y)]和[ν(y)]，将其与最小/最大之间的隶属度与非隶属度的值比较。然后，构建新的下、上近似，提出四个模型，即基于优势关系的I型、II型程度粗糙直觉模糊集模型和基于优势关系的I型、II型双论域程度粗糙直觉模糊集模型，讨论这些模型的相关性质。这些模型的边界域缩小了，也降低了模糊熵值。最后，通过实例验证了模型的有效性。

关键词: 程度粗糙集, 双论域, 直觉模糊集, 优势关系, 模糊熵