An analysis of Fermatean fuzzy graph and its application in a car company

Fuzzy graphs find numerous applications in real life. One of the extensions of fuzzy graphs is Fermatean fuzzy graphs. Here, we introduce the concepts of Fermatean fuzzy set to the domain of graph theory and obtain a novel type of graph, referred to as Fermatean fuzzy graph ( FFG ). The article establishes fundamental terms such as strong FFG , complete FFG , regular FFG , path, degree, total degree, homomorphism, and isomorphism of FFG , as well as the complement of FFG . Alongside the introduction of these concepts, their important properties, theorems, and illustrative examples are defined and discussed. Finally, an application has surfaced suggesting the utilization of FFG s to scrutinize the key factors affecting the productivity of Tata Motors, paving the way for a comprehensive analysis of the company’s operational efficiency using score function.