双论域上的直觉模糊粗糙集

Intuitionistic Fuzzy Rough Sets over Two Universes

本文给出一种新的双论域上的直觉模糊粗糙集模型,定义的近似算子能够保证被近似集与其上、下近似处于同一论域上。首先,在双论域近似空间中,定义三种直觉模糊集的上、下近似,并研究它们之间的关系。其次,在双论域直觉模糊近似空间中,给出由两个论域上直觉模糊二元关系诱导的单个论域上的直觉模糊二元关系,并进一步给出直觉模糊近似算子的构造性定义及其性质。最后,讨论所定义的近似算子与已有定义的近似算子的联系。

This paper presents a new model of intuitionistic fuzzy rough sets over two universes. The approximation operators defined in this paper can guarantee approximated sets and their upper and lower approximations to be on the same universe. Three pairs of approximation operators with respect to an approximation space over two universes are first defined, and their relationships are clarified. An intuitionistic fuzzy relation on a single universe induced by an intuitionistic fuzzy relation on two different universes is then constructed. A pair of intuitionistic fuzzy approximation operators are further defined, and their properties are examined. Finally, connections between our new intuitionistic fuzzy approximation operators with existing ones are discussed.