aspg-21-2745-1791475485 20261008160445 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 24 2 Shawkat Alkhazaleh 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 Belal Batiha Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan Rawan Almarashdeh Department of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan 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 131 146 2745 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.240212 https://www.americaspg.com/journal/21/article/2745 https://www.americaspg.com/storage/11714538371.pdf