International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1974 2020 2020 College of Computing, Informatics and Media, UiTM Cawangan Negeri Sembilan, Kampus Seremban, 73000 Negeri Sembilan, Malaysia Jamiatun Nadwa Ismail College of Computing, Informatics and Media, UiTM Cawangan Negeri Sembilan, Kampus Seremban, 73000 Negeri Sembilan, Malaysia Zahari Rodzi Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq Faisal Al Al-Sharqi Basic Sciences Department, Preparatory Year Deanship, King Faisal University, Al-Ahsa 31982, Saudi Arabia Ashraf Al Al-Quran College of Computing, Informatics and Media, UiTM Cawangan Kelantan, Kampus Machang, 18500, Kelantan, Malaysia Hazwani Hashim College of Computing, Informatics and Media, UiTM Cawangan Selangor, Kampus Dengkil, 43800 Selangor, Malaysia Nor Hashimah Sulaiman 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 2023 127 134 10.54216/IJNS.210412 https://www.americaspg.com/articleinfo/21/show/1974