aspg-21-1974-1791475247 20261008160047 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2023 21 4 Jamiatun Nadwa Ismail College of Computing, Informatics and Media, UiTM Cawangan Negeri Sembilan, Kampus Seremban, 73000 Negeri Sembilan, Malaysia Zahari Rodzi College of Computing, Informatics and Media, UiTM Cawangan Negeri Sembilan, Kampus Seremban, 73000 Negeri Sembilan, Malaysia Faisal Al-Sharqi Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq Ashraf Al-Quran Basic Sciences Department, Preparatory Year Deanship, King Faisal University, Al-Ahsa 31982, Saudi Arabia Hazwani Hashim College of Computing, Informatics and Media, UiTM Cawangan Kelantan, Kampus Machang, 18500, Kelantan, Malaysia Nor Hashimah Sulaiman College of Computing, Informatics and Media, UiTM Cawangan Selangor, Kampus Dengkil, 43800 Selangor, Malaysia Pythagorean neutrosophic sets (PNS) have been recognized as a highly effective mechanism for managing situations characterized by indeterminacy and inconsistency within decision-making procedures. This paper delves into the examination of algebraic operations performed on PNS, thereby expanding their scope of application, and enhancing their utility. In this study, we put forth a set of algebraic operations that can be applied to PNS. These operations encompass addition, multiplication, scalar multiplication, and power. These operations facilitate the efficient manipulation and combination of PNS, thereby enhancing decision-making in scenarios characterized by uncertainty and vagueness. To demonstrate the efficacy of these operations, we will present several illustrative examples accompanied by corroborating proofs. The introduction of algebraic operations enhances the capabilities of PNS, thereby creating opportunities for their practical application. 2023 127 134 1974 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.210412 https://www.americaspg.com/journal/21/article/1974 https://www.americaspg.com/storage/71690960489.pdf