Numerous bounds and significance of the Sombor index in fuzzy graph

The topological index is a useful tool in mathematical chemistry that connects a numerical value to a network structure. The Sombor index is well-known for establishing such connections. This work presents the generalization of the Sombor index from a fuzzy point of view. We introduce the Sombor index for fuzzy graphs ( \(SO(FG)\) $SO(FG)$ ). Some crucial bounds of \(SO(FG)\) $SO(FG)$ are established for numerous graph operations, including Cartesian product, composition, join, and union. In addition, we find the relationship between the Sombor index and other topological indices. Moreover, we present an application of the Sombor index for fuzzy graphs to identify the most alarming type of cancer in India, which clearly justifies the generalization of the Sombor index.