Bipolar Neutrosophic Transportation Problem in Symmetric Graphs

The breadth of transportation problems (TP) makes them applicable to real-world scenarios. Real-world issues are often unforeseen, making it impossible to estimate a specific cost. Fuzzy and intuitionistic fuzzy sets resolve uncertainty, but have severe limitations. To solve these challenges, bipolar neutrosophic sets (BNS) generalize fuzzy sets, crisp sets, and intuitionistic fuzzy sets, effectively handling ambiguous, unpredictable, and insufficient information in real-world scenarios. Using BNS provides a more dependable, precise, and trustworthy procedure than conventional methods. In this paper, we use a symmetric graph network to find the shortest path for a bipolar neutrosophic transit problem. The approach is utilized to address bipolar neutrosophic transportation network issues with a single-valued neutrosophic network problems. This integration improves transportation problem-solving skills, providing more precision and reliability. The novel technique serves a variety of businesses, including logistics and supply chain management. By delivering accurate solutions, BNS assists decision-makers in optimizing transportation networks, reducing costs, and increasing efficiency. Our findings show that BNS has the ability to address real-world transportation difficulties by providing a helpful tool for managing uncertainty and complexity, hence contributing to more dependable systems. This study helps design more effective transportation systems. This research leads to the creation of more efficient transportation networks, hence increasing operational effectiveness.