不完备信息系统中Rough集的扩充模型

Extension Model of Rough Set under Incomplete Information

经典的Rough集理论所处理的信息系统必须是完备的.为了能够分析处理不完备的信息系统,需要建立新的扩充Rough集模型.对现有的几种比较有影响的Rough集扩展模型进行了分析研究,提出了一种带约束的相似关系Rough集模型,并将这些扩充模型之间的关系进行了分析比较.结果显示,基于约束相似关系的扩充Rough集模型优于基于容差关系的扩充Rough集模型和基于相似关系的扩充Rough集模型,使得对象的划分更加合理,符合人们在处理数据时的直观感觉.

The classical rough set theory is based on complete information systems. The starting point of the rough set theory is an observation that objects with the same description are indiscernible with respect to the available information. It classifies objects using upper and lower-approximation defined on an indiscernihility relation, a kind of equivalent relation. But the indiscemibility relation may be too rigid in some situations. Therefore several generalizations of the rough set theory have been proposed, some of which extend the indiscemibility relation using more general similarity or tolerance relations. Unfortunately, these extensions have their own limitation. In this paper, several extension model of rough set under incomplete information are discussed. A concept of constrained similarity relation as a new extension of rough sets theory is introduced, and the upper-approximation and lower-approximation defined on constrained similarity relation are proposed. Furthermore, the performances of these extended relations are compared also. Analysis result shows that this relation can effectively process incomplete information and generate rational object classes.