Rough集理论在不完备信息系统中的扩充

EXTENSION OF ROUGH SET UNDER INCOMPLETE INFORMATION SYSTEMS

Pawlak教授所提出的经典 Rough集理论主要是针对完备信息系统的 ,利用了不可分辨关系这种等价关系来对对象进行上近似和下近似分类 .对于不完备信息系统的处理 ,需要对经典 Rough集理论进行扩充 ,主要是对不可分辨关系进行扩充 .目前已经有了基于容差关系、相似关系和量化容差关系等的扩充 Rough集理论 .但是 ,这些扩充也还存在一些局限性 ,将提出一种基于限制容差关系的扩充 Rough集模型 ,并比较分析这些扩充 Rough集模型之间的性能 .

The classical rough set theory developed by professor Pawlak is based on complete information systems. It classifies objects using upper-approximation and lower-approximation defined on an indiscernibility relation that is a kind of equivalent relation. In order to process incomplete information systems, the classical rough set theory needs to be extended, especially, the indiscernibility relation needs to be extended to some inequivalent relation. There are several extensions for the indiscernibility relation now, such as tolerance relation, non-symmetric similarity relation, and valued tolerance relation. Unfortunately, these extensions have their own limitation. Presented in this paper is a new extension of rough set based on limited tolerance relation. The performances of these extended rough set models are also compared.