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Interval-valued information systems are generalized models of single-valuedinformation systems. By rough set approach, interval-valued information systemshave been extensively studied. Authors could establish many binary relationsfrom the same interval-valued information system. In this paper, we do someresearches on comparing these binary relations so as to provide numericalscales for choosing suitable relations in dealing with interval-valuedinformation systems. Firstly, based on similarity degrees, we compare the mostcommon three binary relations induced from the same interval-valued informationsystem. Secondly, we propose the concepts of transitive degree and clusterdegree, and investigate their properties. Finally, we provide some methods tocompare binary relations by means of the transitive degree and the clusterdegree. Furthermore, we use these methods to analyze the most common threerelations induced from Face Recognition Dataset, and obtain that $RF_{B}^{\lambda}$ is a good choice when we deal with an interval-valued informationsystem by means of rough set approach.

Comparison research on binary relations based on transitive degrees and cluster degrees