Deep Neural Network-Enhanced Trapezoidal Neutrosophic Shortest-Path Optimization in Uncertain Graphs

Shortest-path optimization is severely hampered in real-world networked systems like communication, logistics, and transportation by node and edge parameter uncertainty. The Deep Neural Network-Enhanced Trapezoidal Neutrosophic Shortest-Path Algorithm (DNN-TNSP), a unique method for effectively computing the shortest path in uncertain weighted graphs, combines deep learning and trapezoidal neutrosophic theory. The suggested approach initially uses Trapezoidal Neutrosophic Numbers (TNNs) to represent graph edge weights in order to account for data imprecision, uncertainty, and inconsistency. Then, by approximating neutrosophic cost distributions and dynamically modifying path weights based on context-sensitive features retrieved from uncertain graphs, a specific Neutrosophic Graph Encoder (NGE) deep neural network is trained to find optimal paths. We benchmark a synthetic transportation network dataset with embedded uncertainty characteristics against common techniques such as Ant Colony Optimization and Dijkstra in fuzzy environments. Under various uncertainty settings, the DNN-TNSP method performs better at finding trustworthy shortest pathways. High prediction accuracy of optimal pathways is indicated by evaluation criteria such as F1 Score (91.5%), Precision (92.3%), and Recall (90.7%). The robustness of the classifier is further confirmed by the Receiver Operating Characteristic (ROC) curve, which shows significant discriminative power between optimal and substandard pathways with an Area under Curve (AUC) of 0.94. By combining deep learning and trapezoidal neutrosophic reasoning, a scalable and flexible framework for intelligent path optimization in intricate, unpredictable environments is created, setting the stage for future developments in robust network design and smart transportation.