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

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.

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

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.

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.

As the realm of artificial intelligence (AI) expands, its societal implications soar. Today, society actively debates its rollout – yet such discourse often permeates news articles and social media unobjectively and without rigorous peer review. The purpose of this paper is to discuss the most pressing concerns associated with AI development and deployment.

This paper proposes a tripartite framework as a strategic guide and guardrail for AI’s evolution.

This robust framework addresses challenges, mitigates potential risks and harnesses AI opportunities for our shared future.

A policy-techno-legal framework for understanding key AI challenges and foundations for building AI guardrails.