Comparison research on binary relations based on transitive degrees and cluster degrees
This work addresses the selection of binary relations for researchers in rough set theory and interval-valued data analysis, but it is incremental as it builds on existing methods.
The paper tackles the problem of comparing binary relations in interval-valued information systems to provide numerical scales for selecting suitable relations, and finds that $RF_{B} ^λ$ is a good choice when applied to the Face Recognition Dataset using rough set approach.
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.