On the classification of Pythagorean fuzzy subgroups of abelian groups

Abstract

Pythagorean fuzzy set is one of the most used tool for depicting uncertainty. A divisible subgroup is among the most significant categories of subgroups of an abelian group. The number of Pythagorean fuzzy subgroups in any group is infinite without a suitable equivalence constraint on the Pythagorean fuzzy sets. To get a meaningful categorization, a sufficient equivalent condition on the collection of all Pythagorean fuzzy subgroups needs to be defined. In this paper, the concept of Pythagorean fuzzy divisible subgroups of a group is introduced. An equivalence relation on Pythagorean fuzzy sets is defined. Several properties of this equivalence relation on Pythagorean fuzzy subgroups are explained. Pythagorean fuzzy subgroups related to their maximal chains are introduced. All possible Pythagorean fuzzy subgroups of finite abelian groups are investigated.