基于一般二元关系的不确定性度量方法研究

Study on Uncertainty Measure Based on General Binary Relation

针对一般二元关系,从知识的区分能力角度提出一种带有可调节参数的新的不确定性度量—α熵,给出了其在一般二元关系下的重要性质,指出一般二元关系下的α熵是现有多种不确定性度量的扩展,统一了完备和不完备信息系统中知识的不确定性度量。结合知识的α熵,给出了一般二元关系下粗糙集的α精度和α粗糙度的定义,证明了α精度、α粗糙度和知识粒度之间的单调关系。实例表明α精度和α粗糙度比经典粗糙度度量更精确,且符合人们的认识规律。这些结论发展了粗糙集的不确定测度理论,为信息系统中以一般二元关系为基础的知识获取提供了理论依据。

From the point of that knowledge can be seen as the ability to perform classifications,a new kind of measurement of rough set,based on general binary relations,was presented.It is found that the α entropy and α accuracy increase monotonously while α roughness decreases monotonously as the information granularities become smaller.By means of the α entropy knowledge,definitions of α accuracy and α roughness were derived,and the α accuracy and α roughness are more reasonable and accurate than those obtained in the classical methods.These results develop the theory of uncertainty and provide theoretical basis for knowledge acquisition in information systems based on general binary relation.