Grey relations

Abstract

Purpose

The goal of this article is to introduce the notion of a grey relation between grey sets using grey numbers.

Design/methodology/approach

This study uses the grey number to create novel ideas of grey sets. We suggest several operations that can be performed on it, including the union, intersection, join, merge, and composition of grey relations. In addition, we present the definitions of reflexive, symmetric, and transitive grey relations and analyze certain characteristics associated with them. Furthermore, we formulate the concept of the grey equivalence relation, apply it to the study of the grey equivalence class over the grey relation, and go over some of its features.

Findings

We present new algebraic aspects of grey system theory by defining grey relations and then analyzing their characteristic features.

Practical implications

This paper proposes a new theoretical direction for grey sets according to grey numbers, namely, grey relations. This paper proposes a new theoretical direction for grey sets according to grey numbers, namely, grey relations. As such, it can be applied to create rough approximations as well as congruences in algebras, topologies, and semigroups.

Originality/value

The presented notions are regarded as new algebraic approaches in grey system theory for the first time. Additionally, some fundamental operations on grey relations are also investigated. Consequently, different types of grey relations, such as reflexive, symmetric, and transitive relations, are discussed. Then, the grey equivalence class derived from the grey equivalence relation is demonstrated, and its properties are examined.

Citation

Atef, M. and Liu, S. (2024), "Grey relations", Grey Systems: Theory and Application, Vol. 14 No. 4, pp. 830-845. https://doi.org/10.1108/GS-03-2024-0031