aspg-21-2818-1791472336 20261008151216 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 24 3 Mourad Oqla Massa’deh Department of Applied science, Ajloun collage, Al-Balqa Applied university, P. O. Box 26816, Jordan Ahlam omar Fallatah Taibah University, College of Science, Department of Mathematics, Madinah, Saudi Arabia In this article, homomorphism and anti-homomorphism bipolar valued multi normal fuzzy HX subgroup of a HX group is studied, discussed and their properties are introduced. The theorems presented in this article are considered a generalization of what has been publishedthrough the concept of fuzzy sets. As the concept of fuzzy sets was introduced by Zadeh in 1965, after that this concept, we expanded into more than one types, intuitionistic fuzzy set, bipolar fuzzy sets, tripolar fuzzy set, and bipolar valued multi fuzzy set are one of this. 2024 165 171 2818 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.240314 https://www.americaspg.com/journal/21/article/2818 https://www.americaspg.com/storage/81716378075.pdf