aspg-21-3629-1791472337 20261008151217 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 26 1 Eman A. AbuHijleh Basic sciences department, Al-Zarqa University College, Al-Balqa Applied University, Amman, Jordan Sara A. Khalil Mathematics Department, Faculty of Science, Applied Science Private University, Amman, Jordan Sana Abu-Ghurra Mathematics Department, Faculty of Science, Applied Science Private University, Amman, Jordan Ghada Alafifi Mathematics Department, Science College, Philadelphia University, Amman, Jordan 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 223 233 3629 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.260119 https://www.americaspg.com/journal/21/article/3629 https://www.americaspg.com/storage/01740197915.pdf