aspg-21-2359-1791475511 20261008160511 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 23 2 Ashraf Al-Quran Basic Sciences Department, Preparatory Year Deanship, King Faisal University, Al-Ahsa 31982, Saudi Arabia Faisal Al-Sharqi Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq; College of Pharmacy, National University of Science and Technology, Dhi Qar, Iraq Hamiden Abd El- Wahed Khalifa Department of Mathematics, College of Science and Arts, Qassim University, Al- Badaya 51951, Saudi Arabia; Department of Operations and Management Research, Faculty of Graduate Studies for St Haifa Alqahtani Department of Statistics and Business Analytics, United Arab Emirates University, UAE Ali M. A. Bany Awad Deanship of Development and Quality Assurance, King Faisal University, Al-Ahsa 31982, Saudi Arabia From fuzzy to neutrosophy, multiple hybrid models have been innovated, with each introduced model surpassing its predecessor. Due to the inherent indeterminacy in the world, a more precise form of imprecision is required. As a result, more sophisticated variants of the neutrosophic set have been created. Examples of these amalgamations include fuzzy neutrosophic sets, intuitionistic fuzzy neutrosophic sets, Pythagorean fuzzy neutrosophic sets, neutrosophic vague sets, and neutrosophic rough sets. The main objective of this paper is to present another variant of the neutrosophic set called T-spherical fuzzy-valued neutrosophic set (T-SFVNS). Serving as a generalization of the aforementioned combinations, T-SFVNS allows for the representation of indeterminacy and inconsistency in a more nuanced manner. In this paper, we define the T-SFVNS and Tspherical fuzzy-valued neutrosophic numbers (T-SFVNNs). Additionally, we propose several types of score and accuracy functions to compare the T-SFVNNs. We also present the basic operations of T-SFVNSs and the algebraic operations of T-SFVNNs, supported by proofs and illustrative examples.. 2024 104 115 2359 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.230209 https://www.americaspg.com/journal/21/article/2359 https://www.americaspg.com/storage/61709912716.pdf