International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3962 2020 2020 Department of Studies and Planning, University of Anbar, Ramadi, Anbar, Iraq Faisal Faisal College of Applied Sciences-Hit, University of Anbar, Iraq Methaq A. Abdlwahid Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, Anbar, Iraq Fawzi Noori Nassar Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, Anbar, Iraq Faisal Al Al-Sharqi Group theory is one of the significant parts of mathematical algebra. This theory is characterized by its ability to address various applications, including the classification of the symmetry of crystals, atoms, molecules, and polyhedral structures. In this work, we study a newly introduced concept, namely BIVFSs, which is an extension of previous concepts discussed in the previous studies section of this work. In this work, we establish and apply basic algebraic concepts applicable to this concept. We combine this concept with group theory, which has important properties and applications, generating important results, which are explained in the third section of this work. An important result of this work is BIVF-level set, support, BIVF-kernel and bipolar BIVF- characteristic function, and BCF point. Then, we interpret the BIVF-subgroup. Furthermore, we present the associated examples and theorems and prove these associated theorems. 2026 2026 85 92 10.54216/IJNS.270108 https://www.americaspg.com/articleinfo/21/show/3962