Subgroups and Homomorphism Structures of Complex Pythagorean Fuzzy Sets

Abstract

This research introduces the notion of complex Pythagorean fuzzy subgroup (CPFSG). Both complex fuzzy subgroup (CFSG) and complex intuitionistic fuzzy subgroup (CIFSG) have significance in assigning membership grades in the unit disk in the complex plane. CFSG has a limitation solved by CIFSG, while CIFSG deals with a limited range of values. The important novelty of the CPFSG lies in its ability to solve the above limitations simultaneously and gets a wider range of values to be engaged in CPFSG. This work has introduced and investigated CPFSG as a new algebraic structure via the conditions that the sum of the square membership and non-membership lies on the unit interval for both the amplitude term and phase term. The result as any CIFSG is CPFSG but the convers is not true has been proved. Complex Pythagorean fuzzy coset has been defined and complex Pythagorean fuzzy normal subgroup (CPFNSG) and their algebraic characteristic has been demonstrated. Homomorphism on the CPFSG is shown. Some results as the inverse image of CPFSG and CPFNSG under isomorphism function are also a CPFSG and CPFNSG, respectively.