International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/4192 2020 2020 Research Scholar, Nirmala College for women, Coimbatore, India J. J. Assistant Professor, Department of Mathematics, Nirmala College for women, Coimbatore, India F. Nirmala Irudayam This study introduces the innovative idea of associating a possibility measure with the membership of an element in a set, and further proposes the structure of quadripartitioned neutrosophic cubic sets (PQNCS). Within this framework, the authors define four distinct components—truth, contradiction, ignorance, and falsity—each in two modes: internal and external. They explore the corresponding sets (truth-internal, contradiction-internal, ignorance-internal, falsity-internal and truth-external, contradiction-external, ignorance-external, falsity-external) and uncover their interrelated properties. Moreover, the work emphasizes the role of a score function as a central instrument for multi-attribute decision-making, and examines how measures of PQNCS—through score, accuracy and certainty functions grounded in the possibility concept—can be employed to support and guide decision-making in the quadripartitioned neutrosophic cubic setting. 2025 2025 348 360 10.54216/IJNS.260429 https://www.americaspg.com/articleinfo/21/show/4192