Single-valued neutrosophic fuzzy Sombor numbers and their applications in trade flows between different countries via sea route

Numerous domains, including all branches of science and technology, database theory, data mining, neural networks, expert systems, cluster analysis, control theory, and image capture, have employed graph theory, which can be used to represent interactions among multiple individuals. An extension of fuzzy sets, specifically intuitionistic fuzzy sets, is the concept of single-valued neutrosophic sets. We extend to graphs the notion of single-valued neutrosophic sets, which is an instance of neutrosophic sets. Neutrosophic fuzzy graphs are generalizations of fuzzy graphs, intuitionistic fuzzy graphs, and interval-valued fuzzy graphs. When in the case of fuzzy or intuitionistic fuzzy graphs relation between atoms in problems is indeterminate, then the neutrosophic fuzzy graph serves as a potent tool for dealing with partial, ambiguous, and inconsistent information in the actual world. In single-valued neutrosophic fuzzy graphs, each vertex is allocated a triplet in which the first element represents membership value, second and third elements as indeterminacy and non-membership value, respectively. In this work, we generalize the conclusions relating crisp graphs and fuzzy graphs by applying graph theory to single-valued neutrosophic sets and exploring a novel type of graph structure known as single-valued neutrosophic graphs. Sombor numbers are an effective and efficient tool in describing the topology of the graph in a numerical value. The main aim of this article is to define the first six Sombor numbers for single-valued neutrosophic fuzzy graphs. Then, degree of vertices of different graph families is determined in single-valued neutrosophic fuzzy framework and calculate the six Sombor numbers for these fundamental graph families for single-valued neutrosophic fuzzy graphs. In the end, an application to show the trade flows between different countries via sea route is presented to prove that single-valued neutrosophic fuzzy graphs are more generalized and efficient. First, we calculated the six Sombor numbers for crisp graph and then in SVNS fuzzy framework. Illustrated cases are then provided to show the applicability, viability, efficacy, and benefits of the suggested ways.