基于集对分析的变精度粗糙集模型

Variable Precision Rough Set Model Based on Set Pair Analysis

粗糙集理论是一种新的处理模糊和不确定性知识的数学工具,在人工智能及数据挖掘等众多领域已经得到了广泛的应用。对于不完备信息系统目前也有多种扩充方法,如基于容差关系的扩充、基于相似关系的扩充等等。该文是在集对粗糙集模型的基础上,引入相对分类错误率的概念,提出了一种基于集对分析的变精度粗糙集模型。然后用集对分析的方法得到了变精度的上、下近似的性质,将经典粗糙集理论和集对粗糙集理论进行了推广。最后,通过一个不完备信息系统的具体例子,说明了这种基于集对分析的变精度粗糙集模型对不完备信息系统中处理模糊和不确定性知识的可行性和有效性。

Rough set theory is emerging as a powerful tool for dealing with vagueness and uncertainty of facts,which has important applications to artificial intelligence and data mining.In order to process incomplete information systems,the classical rough set theory needs to be extended.Now there are several extensions such as tolerance relation,similarity relation.In this paper,variable precision rough set model based on set pair analysis is proposed by introducing a concept of relatively classified fault rate.Some properties of the upper approximation and the lower approximation are generalized by set pair analysis.By an example,it is verified that it is more feasible and effective than the previous models in practice.