An Approach to Lagrange’s Theorem in Pythagorean Fuzzy Subgroups

The Pythagorean fuzzy environment is a modern way of depicting uncertainty. The concept of Pythagorean fuzzy semi-level subgroups of any group is described in this paper. The Pythagorean fuzzy order of an element in a Pythagorean fuzzy subgroup is introduced and established various algebraic attributes. The relation between the Pythagorean fuzzy order of an element of a group and the order of that group is established. The Pythagorean fuzzy normalizer and Pythagorean fuzzy centralizer of Pythagorean fuzzy subgroups are discussed. Further, the concept of Pythagorean fuzzy quotient group and the index of a Pythagorean fuzzy subgroup are defined. Finally, a framework is developed for proving Lagrange’s theorem in Pythagorean fuzzy subgroups.