Granularity measures and rough approximation measures are two basic methods for dealing with uncertainty in rough set theory. Interval-valued information tables are a generalization of single-valued information tables. In this paper, we study granularity measures and rough approximation measures in interval-valued information tables based on kernel similarity relations. More specifically, we propose a new type of similarity relations called kernel similarity relations by employing kernel functions to compute the similarity between objects in interval-valued information tables. Based on the kernel similarity relations, we introduce a class of average granularity measures, from which we can obtain some specific granularity measures in interval-valued information tables. We develop three rough approximation measures in interval-valued information tables based on the kernel similarity relations, including kernel accuracy measure, kernel roughness measure, and kernel approximation accuracy measure. By using the class of average granularity measures, we further examine three granularity-based rough approximation measures in interval-valued information tables. The results of the experimental analysis provide an insightful understanding of the essence of the proposed granularity measures and rough approximation measures in interval-valued information tables.

粒度度量和粗糙逼近度量是处理粗糙集理论中不确定性的两种基本方法。间隔值信息表是单值信息表的概括。本文研究了基于核相似度关系的区间值信息表中的粒度度量和粗略近似度量。更具体地说，我们通过利用核函数计算区间值信息表中对象之间的相似度，提出了一种新型的相似度关系，称为核相似度关系。基于核相似度关系，引入一类平均粒度度量，从中可以得到区间值信息表中的一些特定粒度度量。基于核相似度关系，我们在区间值信息表中开发了三种粗略近似度量，包括核精度度量，核粗糙度度量和核近似精度度量。通过使用平均粒度度量的类别，我们进一步检查了间隔值信息表中的三种基于粒度的粗略近似度量。实验分析的结果提供了对间隔值信息表中所提出的粒度度量和粗略近似度量的本质的深刻理解。我们进一步研究了间隔值信息表中的三种基于粒度的粗略近似度量。实验分析的结果提供了对间隔值信息表中所提出的粒度度量和粗略近似度量的本质的深刻理解。我们进一步研究了间隔值信息表中的三种基于粒度的粗略近似度量。实验分析的结果提供了对间隔值信息表中所提出的粒度度量和粗略近似度量的本质的深刻理解。