一种广义直觉模糊粗糙集模型

Generalized Intuitionistic Fuzzy Rough Set Model

Atanassov直觉模糊集是对Zadeh模糊集最有影响的一种扩充和发展。为进一步拓展Pawlak粗糙集对多重不确定性信息的处理能力,将直觉模糊集引入粗糙集,采用构造性方法提出了一种广义直觉模糊粗糙集模型。首先,介绍了直觉模糊集在一个特殊格上的等价定义,对直觉模糊近似空间的两个基本要素(直觉模糊逻辑算子和直觉模糊关系)进行了研究,证明了一些重要的性质定理;在此基础上,建立了等价关系下的直觉模糊粗糙集模型;最后,对所提模型的性质进行了分类验证与讨论。

Intuitionistic fuzzy set,proposed by Atanassov,is one of the most influential generalizations of Zadeh’s fuzzy sets.To extend the capability of Pawlak’s rough set theory in processing multiple uncertainties,intuitionistic fuzzy set and rough set were combined and a general model of intuitionistic fuzzy rough set was discussed by using constructive approach.Firstly,an equivalent definition of intuitionistic fuzzy set on a special lattice was introduced.Secondly,several important properties of intuitionistic fuzzy logic operators and intuitionistic fuzzy relation which are the two fundamental elements of intuitionistic fuzzy approximation space were proved,and then the model of intuitionistic fuzzy rough sets was constructed.Finally,the properties of proposed model were classified and examined respectively.