The Introduction to the Conjugate of an Intuitionistic Multi L–Fuzzy Subgroup and the Strongest Intuitionistic Multi L–Fuzzy Relation

Abstract

In this paper, the theory of intuitionistic multi L-fuzzy subgroups plays a significant role in extending classical group theory under uncertainty. In this work, we introduce the notion of the conjugate of an intuitionistic multi L–fuzzy subgroup and establish its fundamental properties in relation to group operations. This concept provides a deeper understanding of subgroup behavior under conjugation while accounting for multiple levels of membership, non-membership, and hesitation. Furthermore, we define the strongest intuitionistic multi L–fuzzy relation and explore its role in preserving the structural characteristics of fuzzy subgroups. These two notions together enrich the algebraic framework of intuitionistic multi L-fuzzy theory, laying a foundation for both theoretical development and practical applications in decision making, information processing, and related fields.