基于边界域和知识粒度的粗糙集不确定性度量

为了克服现有作积形式不确定性度量方法的缺陷, 基于边界域提出一种用改进粗糙度和知识粒度求和形式的粗糙不确定性度量公式. 与现有方法相比, 它同时考虑了由边界域和知识粗糙性产生的不确定性, 从理论上证明了集成后的不确定性度量值确实比单个影响因素产生的不确定性度量值大, 是一种更加合理的不确定性度量方法. 将该方法推广到基于严凸函数知识粒度情形, 得到一类度量粗糙集不确定性度量方法, 并研究了随划分变细时, 粗糙 度、改进粗糙度与所提出方法之间的关系. 最后设计了一组算例对它们进行比较, 比较结果表明, 所提出的方法对划分变细更加敏感.

Uncertainty measures of rough sets based on boundary region and knowledge granularity

To overcome the defect of product form methods, an uncertainty measure integrating modified rough measure and knowledge granularity is proposed, which can simultaneously describe the uncertainties resulted from the boundary region and knowledge roughness. It is theoretically proved that more values are got after integrating than that produced by only one effective factor, so the proposed method is more reasonable than the existing methods. Then the similar methods are generalized to the knowledge granularity reduced from strictly concave functions. The relationship among the rough measure, the modified rough measure and the proposed method is discussed with respective to the refinement of partition. Finally, a group of examples are designed to compare them. The results show that the proposed method is more sensitive to the refinement of partition.