aspg-21-2154-1791472100 20261008150820 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2023 22 3 Yousef Al-Qudah Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, Jordan Faisal Al-Sharqi Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq hand the idea of interval-valued neutrosophic soft sets (IVNSSs) is a new generalization of the neutrosophic soft sets to the neutrosophic sets when the authors combine the critical features of IVNS and soft sets (SSs) in one model. Accordingly, this model worked to provide decision-makers with more flexibility in the process of interpreting uncertain information. From a scientific point of view, the process of evaluating this highperformance IVNSS disappears. Therefore, in this paper, we initiated a new approach known as possibility interval-valued neutrosophic soft sets (PIVNSSs) as a new development in a fuzzy soft computing environment. We investigate some fundamental operations on PIVNSSs along with their basic properties. Also, we investigate AND and OR operations between two PIVNSSs as well as several numerical examples to clarify the above fundamental operations. Finally, we have given similarity measure (SM) between two PIVNSSs to construct a new algorithm that is used to demonstrate the effectiveness of the method in handling some real-life applications. 2023 69 83 2154 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.220305 https://www.americaspg.com/journal/21/article/2154 https://www.americaspg.com/storage/21697524764.pdf