Intuitionistic level subgroups in the Klein-4 group

Abstract

A BSTRACT . In this paper we check the status of the already known result “level subgroups of any fuzzy subgroup of a finite group forms a chain” in Intuitionistic Fuzzy environment. The tool we use for this is the Klein-4 group V , which is a non-cyclic group. We prove that V has 64 distinct Intuitionistic Fuzzy Subgroups (IFSGs) upto isomorphism. The Intuitionistic Level Subgroups (ILSGs) of only 40 among them form chains and so the result is not true in intuitionistic fuzzy case. To strengthen our findings we provide a python program to construct the geometric representations of all the 64 IFSGs and its output.