Comprehensive Decision-Making with Spherical Fermatean Neutrosophic Sets in Structural Engineering

P. Roopadevi1, M. Karpagadevi1, S. Krishnaprakash2,∗, Said Broumi3, S. Gomathi4

1Department of Mathematics, Sri GVG Visalakshi College for Women-642128, India

2Department of Mathematics, Sri Krishna College of Engineering and Technology-641008, India

3Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca,

India

4Department of Mathematics, Dr. Mahalingam College of Engineering and Technology-642003, India

Emails: roopakodish@gmail.com; karpagadevi.n@gmail.com; mskrishnaprakash@gmail.com;

broumisaid78@gmail.com; gomathiprakash2013@gmail.com

Abstract

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.

Keywords : Fermatean neutrosophic sets; Extension of Fermatean neutrosophic sets; Spherical Fermatean neutrosophic sets