International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3632 2020 2020 Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, 11953, Jordan Yousef Yousef Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, 11953, Jordan Yousef Al Al-Qudah Department of Mathematics, Faculty of Science and Health, Koya University, Danielle Mitterrand Boulevard, Koya, Kurdistan Region-F.R. KOY45, Iraq Abdulqader O. Hamadameen Artificial Intelligence Sciences Department, College of sciences, Al-Mustaqbal University , 51001,Babil, Iraq R.H. Al Al-Obaidi Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, 11953, Jordan Abdullah S. Al Al-Jawarneh Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, 55431, Iraq; College of Pharmacy, National University of Science and Technology, Dhi Qar, Iraq Faisal Al Al-Sharqi Ministry of Education, Amman, Jordan Anas Owledat In this careful study , through the concept possibility interval valued neutrosophic hyper soft set (abbreviated as piv-NHSS) which is combined from the hypersoft set (HSS) and Interval-valued neutrosophic set under the posobolity degree and each iv-NHSS is assigned a possibility degree in the interval [0, 1]. Based on this concept, we present a more flexible, expanded method for a previous concept named possibility interval valued neutrosophic hyper soft matrix (piv-NHSM) as a new generalization of piv-NHSS. In this work, we also present nseveral algebraic operations and also all the mathematical properties associated with this model. In addition to the above, we have presented a clear algorithm based on the matrix properties of this model, which has been used to solve one of the multi-property decision-making problems. Finally, the correlation coefficient for this concept was defined and explained in detail according to an approved mechanism, with a numerical example provided to illustrate the mechanism of use. Moreover, we develop a new algorithm for solving the decision-making issue based on the proposed correlation coefficient for piv-NHSS . 2025 2025 254 265 10.54216/IJNS.260122 https://www.americaspg.com/articleinfo/21/show/3632