On the Picture Fuzzy Abelian Subgroups of a Group

Abstract

This paper investigates the concept of picture fuzzy subgroups within the framework of group theory. A picture fuzzy subgroup of a group is studied by extending classical subgroup properties to the picture fuzzy environment through positive, neutral, and negative membership degrees. Furthermore, the notions of a picture fuzzy abelian subgroup and a cyclic picture fuzzy subgroup of a group G are introduced as special classes of picture fuzzy subgroups. This picture fuzzy abelian subgroup preserves the commutativity property in the fuzzy sense. Several characterisations and fundamental properties of both picture fuzzy abelian subgroups and cyclic picture fuzzy subgroups are established. The study contributes to the development of picture fuzzy algebra and provides a foundation for further investigations.