aspg-21-2860-1791475935 20261008161215 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 24 4 Shawkat Alkhazaleh Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan Belal Batiha Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan Areen Al-khateeb Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan Hamzeh Zureigat Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan; Applied Science Research Center, Applied Science Private University, Al-Arab St. 21, Amm Abedallah Al-shboul Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan Khaldoun Batiha Department of CS, Faculty of IT, Philadelphia University, Amman 19392, Jordan In this paper, we introduce the concept of Possibility Fermatean Neutrosophic Soft Set and define some related concepts such as Possibility Fermatean Neutrosophic Soft subset, Possibility Fermatean Neutrosophic Soft null set, and Possibility Fermatean Neutrosophic Soft universal set. Then, we define set-theoretical operations of Possibility Fermatean Neutrosophic Soft Sets such as union, intersection, and complement, and investigate some properties of these operations. We also introduce AND-product and OR-product operations between two Possibility Fermatean Neutrosophic Soft Sets. We propose a decision-making method called the Possibility Fermatean Neutrosophic Soft decision-making method (PFNS-decision-making method) which can be applied to decision-making problems involving uncertainty based on AND-product operation. We finally give a numerical example to display the application of the method that can be successfully applied to the problems. 2024 105 125 2860 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.240408 https://www.americaspg.com/journal/21/article/2860 https://www.americaspg.com/storage/51717401258.pdf