Algebraic Operations on Pythagorean neutrosophic sets (PNS): Extending Applicability and Decision-Making Capabilities

Jamiatun Nadwa Ismail¹, Zahari Rodzi^1*, Faisal Al-Sharqi², Ashraf Al-Quran³, Hazwani Hashim⁴, Nor Hashimah Sulaiman⁵

¹College of Computing, Informatics and Media, UiTM Cawangan Negeri Sembilan, Kampus Seremban, 73000 Negeri Sembilan, Malaysia

²Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq

³Basic Sciences Department, Preparatory Year Deanship, King Faisal University, Al-Ahsa 31982, Saudi Arabia

⁴College of Computing, Informatics and Media, UiTM Cawangan Kelantan, Kampus Machang, 18500, Kelantan, Malaysia

⁵College of Computing, Informatics and Media, UiTM Cawangan Selangor, Kampus Dengkil, 43800 Selangor, Malaysia

Emails: ismail.nadwa@gmail.com; zahari@uitm.edu.my; faisal.ghazi@uoanbar.edu.iq; aalquran@kfu.edu.sa; hazwanihashim@uitm.edu.my; nhashima@tmsk.uitm.edu.my

Abstract

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.

Keywords: Pythagorean Neutrosophic Set; Algebraic Operations; decision making; addition; multiplication; scalar multiplication.