International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2745 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 Areen Al .. Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan Hamzeh .. Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan Belal .. Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan Rawan Almarashdeh In this study, we introduce a new concept by making Possibility Fermatean fuzzy soft sets into a more general concept, namely Intuitionistic Possibility Fermatean fuzzy soft sets. We present examples of the application of this theory to a decision-making problem. From a theoretical point of view, we review the basic properties of this model and define the operations essential to its framework. Comprehensive definitions of complement, union, and intersection, as well as AND and OR operations are meticulously presented. As a transition from theory to practical application within this innovative context, we present an algorithm for solving decision-making problems, contributing to the practical implementation of this extended concept. This research aims to improve our understanding of the intuitionistic possibility of Fermatean fuzzy soft sets and to bridge the gap between theoretical advances and their real-world utility in decision-making problems. 2024 2024 131 146 10.54216/IJNS.240212 https://www.americaspg.com/articleinfo/21/show/2745