The Properties of Intuitionistic Multi L–Fuzzy Cosets And Pseudo Intuitionistic Multi L-Fuzzy Cosets of an Intuitionistic Multi L- Fuzzy Subgroup Under Homomorphism and Anti – Homomorphism

In this paper, we introduce and study the concepts of Intuitionistic Multi L - fuzzy cosets and Pseudo Intuitionistic Multi L – fuzzy cosets of an Intuitionistic Multi L – fuzzy subgroup under group homomorphisms and anti-homomorphisms. We investigate the structural properties of these newly defined cosets and explore their relationships with Intuitionistic Multi L – fuzzy subgroups. Furthermore, we analyze the preservation of Intuitionistic Multi L- fuzzy membership and non-membership functions under homomorphic and anti-homomorphic mappings, establishing several fundamental results. Our findings extend classical coset theory to the framework of Intuitionistic Multi L- fuzzy algebraic structures, providing deeper insights into their algebraic behaviour.