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.