International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2153 2020 2020 Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq Faisal Al Al-Sharqi Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia Ashraf Al Al-Quran College of Pharmacy, National University of Science and Technology, Dhi Qar, Iraq Noor Kareem Assi Halaf Curricula and Teaching Methods Department, College of Education, King Faisal University, Al-Ahsa 31982,Saudi Arabia Mona Aladil University Headquarter, Department of Scholarships and Cultural Relations, University Of Anbar, Ramadi, Anbar, Iraq Maha M. Rasheed Soft set(SS) is one of the soft computing techniques that plays an important role in addressing the hiddenness and uncertainty associated with uncertain data. In other 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 high-performance 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 distance measures (DM) 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 53 68 10.54216/IJNS.220304 https://www.americaspg.com/articleinfo/21/show/2153