A certain algebraic structure of bipolar single value neutrosophic  subgroups and its essential properties

Yousef Al-Qudah; Abdullah Alsoboh; Eman Hussein; Faisal Al-Sharqi; Abdullrahman A. Al Maqbali

Authors

Yousef Al-Qudah Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, 11953, Jordan;
Abdullah Alsoboh Department of Basic and Applied Sciences, College of Applied and Health Sciences, A’Sharqiyah University, Post Box No. 42, Post Code No. 400, Ibra, Sultanate of Oman;
Eman Hussein Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, 11953, Jordan;
Faisal Al-Sharqi Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, 55431, Iraq;
Abdullrahman A. Al Maqbali Department of Basic and Applied Sciences, College of Applied and Health Sciences, A’Sharqiyah University, Post Box No. 42, Post Code No. 400, Ibra, Sultanate of Oman;

Keywords:

Neutrosophic set; single-valued neutrosophic set; bipolar single-valued neutrosophic; bipolar single-valued neutrosophic group; bipolar single-valued neutrosophic normal group; homomorphism

Abstract

The idea of bipolar single value neutrosophic set was created as an extension of a single
value neutrosophic set when every single value neutrosophic membership function has two poles.
In this study, we apply this idea in an algebraic environment when we initiate the novel concept of
bipolar single value neutrosophic subgroups and prove that every bipolar single value neutrosophic
subgroup generates two bipolar single value neutrosophic subgroups. we explain the level set,
support, kernel for bipolar single value neutrosophic set, bipolar single value neutrosophic
characteristic function, and bipolar single value neutrosophic point. Then, we illuminate the bipolar
single value neutrosophic subgroup, bipolar single value neutrosophic normal subgroup, bipolar
single value neutrosophic conjugate, normalizer for bipolar single value neutrosophic subgroup,
bipolar single value neutrosophic abelian subgroup, and bipolar single value neutrosophic factor
group. Furthermore, we present the linked theorems and examples and prove these theorems.
Finally, we discussed the image and pre-image of bipolar single-value neutrosophic subgroups
under homomorphism and proved the related theorems.

DOI: 10.5281/zenodo.16343958