Pythagorean Neutrosophic Triplet Groups

Madad Khan; Muhammad Zeeshan; Saima Anis; Florentin Smrandache

Authors

Madad Khan Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Pakistan;
Muhammad Zeeshan Department of Mathematics, COMSATS University Islamabad, Islamabad Campus, Pakistan
Saima Anis Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Pakistan
Florentin Smrandache Department of Mathematics and Sciences, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA;

Keywords:

Neutrosophic triplet, Pythagorean neutrosophic triplet, Neutrosophic triplet group, Pythagorean neutrosophic triplet group.

Abstract

It is a well-known fact that groups are the only algebraic structures having a single binary
operation that is mathematically so perfect that it is impossible to introduce a richer structure
within it. The main purpose of this study is to introduce the notion of the Pythagorean
neutrosophic triplet (PNT) which is the generalization of neutrosophic triplet (NT). The PNT is an
algebraic structure of three ordered pairs that satisfy several properties under the binary operation
(B-Operation)
"
"
. Furthermore, we used the PNTs to introduce the novel concept of a
Pythagorean neutrosophic triplet group (PNTG). The algebraic structure (AS) of PNTG is different
from the neutrosophic triplet group (NTG). We discussed some properties, related results, and
particular
examples of these novel concepts. We further studied Pythagorean
neutro-homomorphism, Pythagorean neutro-isomorphism, etc., for PNTGs. Moreover, we
discussed the main distinctions between the neutrosophic triplet group (NTG) and the PNTG.

DOI: 10.5281/zenodo.11206321