International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2860 2020 2020 Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan Areen Areen 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 Al-khateeb 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, Amman, 11931, Jordan Hamzeh .. Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan Abedallah Al .. Department of CS, Faculty of IT, Philadelphia University, Amman 19392, Jordan Khaldoun Batiha 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 2024 105 125 10.54216/IJNS.240408 https://www.americaspg.com/articleinfo/21/show/2860