aspg-21-3632-1791465328 20261008131528 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 26 1 Eman Hussein Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, 11953, Jordan Yousef Al-Qudah Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, 11953, Jordan Abdulqader O. Hamadameen Department of Mathematics, Faculty of Science and Health, Koya University, Danielle Mitterrand Boulevard, Koya, Kurdistan Region-F.R. KOY45, Iraq R.H. Al-Obaidi Artificial Intelligence Sciences Department, College of sciences, Al-Mustaqbal University , 51001,Babil, Iraq Abdullah S. Al-Jawarneh Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, 11953, Jordan Faisal Al-Sharqi 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 Anas Owledat Ministry of Education, Amman, Jordan 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 several 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 254 265 3632 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.260122 https://www.americaspg.com/journal/21/article/3632 https://www.americaspg.com/storage/articles/manuscripts/01M3J2ZZZBP7WBKD348WRK8Y8M.pdf