Recently, many topological indices (TIs) have been introduced for fuzzy graphs (FGs). Numerous characteristics of FGs along with applications have been explored through these indices. Among the other indices, Connectivity index (CI), Wiener index (WI), Zagreb index ( \(ZI_1\) ) and Randic index (RI) are the most important TIs defined for fuzzy graphs (FGs). These indices have been used widely to solve many real world problems in networking, site selection, illegal immigration networks, modeling intra cities journeys etc. In this manuscript, we give a new view of a vertex degree based index termed Sombor index (SI) for fuzzy graphs (FGs). In this context, we also describe several useful indices related to Sombor index such as Sombor coindex, total Sombor index, p-Sombor index etc and explore bounds for them. Several relationships between Sombor index and the other existing indices such as Zagreb index and reciprocal Randic index are also investigated. Moreover, we propose an algorithm to find the shortest path in any network by using Sombor index of fuzzy graphs. Finally, we provide an application of Sombor index for fuzzy graphs towards logistic management supported by a numerical example which ensures the effectiveness and validity of our proposed algorithm.
