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

TL;DR

This paper introduces methods to compare binary relations in interval-valued information systems using transitive and cluster degrees, aiding in selecting suitable relations for data analysis.

Contribution

It proposes the concepts of transitive degree and cluster degree and develops comparison methods for binary relations based on these measures.

Findings

RF_{B} ^{eta} is identified as a good relation choice for face recognition data.

Comparison methods help in selecting appropriate relations in rough set analysis.

The study enhances understanding of relation properties in interval-valued information systems.

Abstract

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.