基于传递度和聚类度的二元关系比较研究
Comparison research on binary relations based on transitive degrees and cluster degrees
摘要：
区间值信息系统是单值信息系统的推广模型。利用粗糙集方法，区间值信息系统得到了广泛的研究。作者可以从同一个区间值信息系统中建立许多二元关系。本文对这些二元关系进行了比较研究，为处理区间值信息系统时选择合适的关系提供了数值尺度。首先，基于相似度，比较了同一区间值信息系统中最常见的三种二元关系。其次，我们提出了传递度和聚类度的概念，并研究了它们的性质。最后，我们提供了一些利用传递度和聚集度来比较二元关系的方法。进一步，我们利用这些方法分析了人脸识别数据中最常见的三种关系，得出了$RF_{B} ^λ$是用粗糙集方法处理区间值信息系统的一个很好的选择。
英文摘要：
Interval-valued information systems are generalized models of single-valued information systems. By rough set approach, interval-valued information systems have been extensively studied. Authors could establish many binary relations from the same interval-valued information system. In this paper, we do some researches on comparing these binary relations so as to provide numerical scales for choosing suitable relations in dealing with interval-valued information systems. Firstly, based on similarity degrees, we compare the most common three binary relations induced from the same interval-valued information system. Secondly, we propose the concepts of transitive degree and cluster degree, and investigate their properties. Finally, we provide some methods to compare binary relations by means of the transitive degree and the cluster degree. Furthermore, we use these methods to analyze the most common three relations induced from Face Recognition Dataset, and obtain that $RF_{B} ^λ$ is a good choice when we deal with an interval-valued information system by means of rough set approach.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
