Generalized Pythagorean Neutrosophic Sets In the Study of Group Theory

Abstract

: In 2019, Jansi et al. present the notion of the Pythagorean neutrosophic set (PNS) as an extension of
a neutrosophic set with dependent neutrosophic components
whenever
     
2 2 2 0 2 A A A        x x x . But due to the more complexity involved in a
decision-making problem, there is a serious need to generalize the PNS for dealing with indeterminate,
incomplete, and inconsistent data present in the belief system. The main objective of this paper is to elicit the
notion of
( , , )    -Pythagorean neutrosophic set as a generalization of PNS. The
( , , )    -PNS provides
a more powerful tool to model the various types of uncertainty with high precision and accuracy. Concerning to
the idea of
( , , )    -PNS, we propose a new
( , , )    -Pythagorean neutrosophic subgroup (PNSG) and
thus investigate some properties based on the proposed subgroup. Moreover, we discuss the impact of
( , , )    -Pythagorean neutrosophic subgroups in solving real-world problems with an aid of a suitable
example