Intuitionistic Level Subgroups in the Dihedral Group D3

Abstract

A well known result in fuzzy group theory states that “level subgroups of any fuzzy subgroup of a finite group form a chain”. We check the validity of this statement in the intuitionistic fuzzy perspective. We do this using Dihedral Group $D_3$, which is a non-cyclic group. We prove that $D_3$ has 100 distinct intuitionistic fuzzy subgroups (IFSGs) upto isomorphism. The intuitionistic level subgroups (ILSGs) of exactly 76 among them make chains, and hence it can be concluded that the result is not true in the intuitionistic fuzzy perspective. We also enlist all the 100 distinct intuitionistic fuzzy subgroups of $D_3$ upto isomorphism.