The Different Kinds of Intuitionistic Multi L – Fuzzy Cosets With Their Interactions in Normality Conditions

In this paper, we introduce and investigate the properties of Intuitionistic Multi L - Fuzzy Cosets, Pseudo Intuitionistic Multi L – Fuzzy Cosets, and Pseudo Intuitionistic Multi L – Fuzzy Double Cosets of an Intuitionistic Multi L – Fuzzy Normal Subgroup of a group G. We introduce the concepts of these fuzzy cosets and examine their structural characteristics under various group operations. We establish necessary and sufficient conditions for an Intuitionistic Multi L – Fuzzy subset to form a normal subgroup and explore its implications in the coset structure. Furthermore, we analyze the relationships between different types of cosets, including their algebraic properties and interactions with normality conditions.