article · European Journal of Pure and Applied Mathematics
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.
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DOI: 10.29020/nybg.ejpam.v19i1.7164
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