International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3035 2020 2020 Department of Mathematics, Sri GVG Visalakshi College for Women-642128, India S. S. Department of Mathematics, Sri Krishna College of Engineering and Technology-641008, India M. Karpagadevi Department of Mathematics, Sri GVG Visalakshi College for Women-642128, India S. Krishnaprakash Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, India Said Broumi Department of Mathematics, Dr. Mahalingam College of Engineering and Technology-642003, India S. Gomathi This study introduces the Spherical Fermatean Neutrosophic Sets (SFNSs), representing a significant advancement in the realm of Neutrosophic Sets (NSs) and Fermatean neutrosophic sets (FNSs). In decision making scenarios involving diverse perspectives, a mere average of decision values may fail to capture the entire spectrum of viewpoints. To address this limitation, the SFNS is proposed as a comprehensive solution. It features a spherical representation that encompasses membership, non-membership and indeterminacy functions at its core, complemented by a defined radius. This spherical construct facilitates the encapsulation of all decision makers’ opinions within its bounds, providing a holistic perspective. Leveraging its geometric structure, the SFNS excels in resolving ambiguity and risk with greater accuracy and effectiveness compared to conventional FNSs. This innovative approach aims to better accommodate the complexities of decision making involving diverse perspectives. Selecting the best material for a structural engineering project is given as numerical example at the end. 2024 2024 432 450 10.54216/IJNS.240433 https://www.americaspg.com/articleinfo/21/show/3035