On Soluble Intuitionistic Fuzzy Group and Its Properties

Abstract

This article introduces the concept of soluble (or solvable) intuitionistic fuzzy groups as a novel intuitionistic fuzzy algebraic structure. Certain fundamental results concerning intuitionistic fuzzy normal subgroups and quotient intuitionistic fuzzy groups are established. Furthermore, a solvable series for an intuitionistic fuzzy group is constructed and illustrated through a detailed example. It is demonstrated that the family of intuitionistic fuzzy subgroups of a given intuitionistic fuzzy group shares the same support as the group itself. Finally, a biconditional relationship between a solvable intuitionistic fuzzy group and its support is proved.