On Soluble Intuitionistic Fuzzy Group and Its Properties - Ejegwa, Paul Augustine; Kausar, Nasreen; Smerat, Aseel; Cagin, Tonguc (NEW YORK BUSINESS GLOBAL LLC, 2026)
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.
Keywords: Intuitionistic fuzzy groups; intuitionistic fuzzy subgroups; intuitionistic fuzzy normal subgroups; quotient intuitionistic fuzzy groups; solvable intuitionistic fuzzy groups; Mathematics