International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3629 2020 2020 Basic sciences department, Al-Zarqa University College, Al-Balqa Applied University, Amman, Jordan admin admin Mathematics Department, Faculty of Science, Applied Science Private University, Amman, Jordan Sara A. Khalil Mathematics Department, Faculty of Science, Applied Science Private University, Amman, Jordan Sana Abu Abu-Ghurra Mathematics Department, Science College, Philadelphia University, Amman, Jordan Ghada Alafifi In this paper, we continue to discuss the concept of harmonized fuzzy subgroups. We present the harmonized fuzzy coset and harmonized fuzzy normal subgroup and their properties. We also study the effect of group homomorphism on harmonized fuzzy subgroups. Finally, we define and study the cartesian product of two harmonized fuzzy subgroups. 2025 2025 223 233 10.54216/IJNS.260119 https://www.americaspg.com/articleinfo/21/show/3629