  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 $RF_{B}
^{\lambda}$ is a good choice when we deal with an interval-valued information
system by means of rough set approach.
