On intuitionistic fuzzy characteristic and Frattini subgroups

This paper presents intuitionistic fuzzy characteristic subgroups and discusses some of its properties. It is established that an intuitionistic fuzzy subgroup of an intuitionistic fuzzy group is characteristic provided its cuts are characteristic subgroups. In addition, it is proven that every intuitionistic fuzzy characteristic subgroup of an intuitionistic fuzzy group is an intuitionistic fuzzy normal subgroup. Furthermore, the notions of intuitionistic fuzzy maximal subgroups and intuitionistic fuzzy Frattini subgroups are established. It is shown that every intuitionistic fuzzy Frattini subgroup is an intuitionistic fuzzy characteristic subgroup as well as an intuitionistic fuzzy normal subgroup, respectively. Finally, some results on intuitionistic fuzzy Frattini subgroups are presented with regards to the level sets and cuts of an intuitionistic fuzzy groups.