集值决策表基于邻域关系的属性约简

Attribute Reduction of Set-valued Decision Tables Based on Neighborhood Relation

集值信息系统是完备信息系统的广义形式,它当中的一些对象在某些属性下的取值可能不止一个,反映的是信息的不确定性。本文在集值信息系统上引入对象的邻域关系,并以每个对象的邻域作为基本集,建立了集值信息系统的粗糙集方法。为了简化的知识表示,我们进一步讨论了邻域协调集值决策表的正域约简与邻域不协调集值决策表的近似分布约简,给出了正域约简与近似分布约简的等价刻画条件,并借助区分函数给出了计算正域约简与近似分布约简的方法。

Set-valued information systems are generalized complete information systems,in which some objects may have more than one value for an attribute that reflecting the uncertainty of the information.In this paper,by introducing a neighborhood relation to set-valued information systems,we establish a rough set approach based on the neighborhood of every object as elementary set.In order to simplify the knowledge representation,we further discuss the positive reduction of neighborhood consistent set-valued decision tables and the approximate distribution reduction of neighborhood inconsistent set-valued decision tables;some sufficient and necessary conditions for a set positive region reduction or approximate distribution reduction were given.Finally,by constructing the discernibility functions,the approaches for positive region reduction and approximate distribution reduction are provided.