International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2818 2020 2020 Department of Applied science, Ajloun collage, Al-Balqa Applied university, P. O. Box 26816, Jordan Mourad Mourad Taibah University, College of Science, Department of Mathematics, Madinah, Saudi Arabia Ahlam omar Fallatah 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 2024 165 171 10.54216/IJNS.240314 https://www.americaspg.com/articleinfo/21/show/2818