A new approach to fuzzy group theory using (α,β)-Pythagorean fuzzy sets.

A Pythagorean fuzzy set (PFS) is a very efficient and powerful tool for handling uncertainty and vagueness. In this paper, we present the notion of (α,β) -Pythagorean fuzzy set (PFS) as a generalisation of Pythagorean fuzzy set (PFS). We propose a new fuzzy subgroup, called (α,β) -Pythagorean fuzzy subgroup (PFSG). We investigate properties of our proposed fuzzy subgroup. We present the concept of (α,β) -Pythagorean fuzzy coset (PFC) and (α,β) -Pythagorean fuzzy normal subgroup (PFNSG). Furthermore, we define (α,β) -Pythagorean fuzzy level subgroup (PFLSG) and establish properties of it. [ABSTRACT FROM AUTHOR]