aspg-21-3035-1791472312 20261008151152 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 24 4 P. Roopadevi1, M. Karpagadevi Department of Mathematics, Sri GVG Visalakshi College for Women-642128, India M. Karpagadevi Department of Mathematics, Sri Krishna College of Engineering and Technology-641008, India S. Krishnaprakash Department of Mathematics, Sri GVG Visalakshi College for Women-642128, India Said Broumi Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, India S. Gomathi Department of Mathematics, Dr. Mahalingam College of Engineering and Technology-642003, India 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 432 450 3035 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.240433 https://www.americaspg.com/journal/21/article/3035 https://www.americaspg.com/storage/91720869664.pdf