A Decision-Making Model for the Travelling Salesman Problem Based on Neutrosophic Edge Connectivity

Neutrosophic edge connectivity is a new idea in graph theory that adds indeterminacy and uncertainty to traditional edge connectivity. It is especially useful for challenging optimization problems that happen in the real world. The use of neutrosophic edge connectivity in solving the well-known NP-hard issue in combinatorial optimization, the Travelling Salesman issue (TSP), is examined in this work. We make a new framework by combining neutrosophic logic, which makes TSP solutions more flexible and realistic, especially in environments that are uncertain and changing quickly, where traditional deterministic models don't work. By taking into account the levels of truth, indeterminacy, and falsity in edge connectivity, the suggested method helps people make better route optimization decisions. Here in this research paper, we provide a thorough theoretical study along with mathematical examples of TSP (Traveling Salesman Problem) situations to verify the method's efficiency. Furthermore, we proposed a problem statement. A logistics business must choose the best delivery path among different cities. It turns out that our neutrosophic based approach makes solutions more stable and opens up a beneficial path for more research in real-world logistics and uncertainty-based optimization.