A Study on AG-Groups in Spherical Fuzzy Environment

Abstract

An AG-group is an algebraic structure that satisfies the left invertive law and includes its left identity and inverse elements. This framework is naturally suited for representing and manipulating various real-life applications in civil engineering, information engineering, artificial intelligence, and more. In this paper, we present the structural application of AG-groups in data encryption and in the rotational transformation of water molecules. Additionally, numerous authors have explored fuzzy set theory over AG-group systems, yielding many valuable results. Spherical fuzzy set theory, an extension of fuzzy set theory, allows for the representation of uncertainty in decision-making, where there may be multiple possible choices or uncertainty about the degree of membership of an element in a set. However, no prior work has combined spherical fuzzy set theory with AG-groups, which motivates our study. In this paper, we apply spherical fuzzy set theory to AG-groups and introduce the concept of spherical fuzzy AG-subgroupoids. We provide the characterization of spherical fuzzy AG-subgroupoids over AG-groupoids and examine their related properties. As an application of spherical fuzzy sets over AG-groups, we develop the concept of normal spherical fuzzy groups over AG-groups and investigate their various properties.