International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2154 2020 2020 Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, Jordan Yousef Al Al-Qudah Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq Faisal Al Al-Sharqi 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 2023 69 83 10.54216/IJNS.220305 https://www.americaspg.com/articleinfo/21/show/2154