二型直觉模糊粗糙集

将二型直觉模糊集和粗糙集理论融合,建立二型直觉模糊粗糙集模型。首先,在二型直觉模糊近似空间中,定义了一对二型直觉模糊上、下近似算子,并讨论了二型直觉模糊关系退化为普通二型模糊关系和一般等价关系时,上、下近似算子的具体变化形式。然后,将普通二型模糊集之间包含关系的定义推广到了二型直觉模糊集,在此基础上研究了二型直觉模糊上、下近似算子的一些性质。最后,定义了自反的、对称的和传递的二型直觉模糊关系,并讨论了这3种特殊的二型直觉模糊关系与近似算子的特征之间的联系。该结论进一步丰富了二型模糊集理论和粗糙集理论,为二型直觉模糊信息系统的应用奠定了良好的理论基础。

Type-2 intuitionistic fuzzy rough sets

In this study, we integrate the theories of type-2 intuitionistic fuzzy sets and rough sets to construct a type-2-intuitionistic-fuzzy-and-rough-sets model. First, in type-2 intuitionistic fuzzy approximation space, we define a pair of type-2 intuitionistic fuzzy upper and lower approximation operators. We then discuss specific changes in these upper and lower approximation operators for a situation in which the type-2 intuitionistic fuzzy relations degenerate into common type-2-fuzzy and general-equivalence relations. Next, we generalize the definition of the inclusion relation between general type-2 fuzzy sets as type-2 intuitionistic fuzzy sets. On this basis, we then explored the properties of type-2-intuitionistic-fuzzy upper and lower approximation operators. We then defined reflexive, symmetric, and transitive type-2 intuitionistic fuzzy relations. Finally, we discuss the relations between these three special type-2 intuitionistic fuzzy relations and the characteristics of their approximation operators. Conclusions drawn in this study further enrich the theories of type-2 intuitionistic fuzzy and rough sets and establish a good theoretical basis for the application of the type-2 intuitionistic fuzzy information system.