International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3635 2020 2020 Research Scholar, Department of Mathematics, Noorul Islam Centre for Higher Education, Thuckalay- 629180, Tamil Nadu, India Mahizha Mahizha Department of Mathematics, Noorul Islam Centre for Higher Education, Thuckalay- 629180, Tamil Nadu, India Immaculate Mary. M. In a neutrosophic environment, a single-valued neutrosophic multi-set, and an intuitionistic fuzzy-valued neutrosophic multi-set are defined by sequences of acceptance, indeterminacy, and rejection grades. The structure of these sets enables the incorporation of multiple layers of information across acceptance, indeterminacy, and rejection grades, making them particularly valuable for multi-criteria decision-making processes. This paper presents the N-valued T-spherical fuzzy neutrosophic set as an advanced extension of neutrosophic sets, aimed at improving uncertainty management and imprecision in complex, real-world scenarios. Building upon previous models such as neutrosophic sets, intuitionistic fuzzy-valued neutrosophic sets, Pythagorean fuzzy neutrosophic sets, and T-spherical fuzzy neutrosophic sets, this new approach introduces greater flexibility in handling indeterminacy. The authors define N-valued T-spherical fuzzy neutrosophic sets and numbers, incorporating new mathematical operations and comparison functions. A significant contribution of the work is the development of simplified neutrosophic-valued distance-based similarity measures for N-valued T-spherical fuzzy neutrosophic sets, along with a score function to rank simplified neutrosophic values. To illustrate the practical utility of this framework, an algorithm is applied to a real-world problem of site selection for solid waste management systems, effectively addressing decision-making scenarios with disjoint criteria. The results and discussions show that the N-valued T-spherical fuzzy neutrosophic set outperforms existing methods by providing more accurate and precise results, specifically in multi-criteria decision-making contexts. The site choice example for solid waste management highlights how this new approach enhances accuracy. 2025 2025 293 310 10.54216/IJNS.260125 https://www.americaspg.com/articleinfo/21/show/3635