A New Approach for Evaluation of Fuzzy Travelling Salesman Problem using Pentagonal Fuzzy Number

The Travelling Salesman Problem (TSP) is a specific kind of task where a salesman commences his journey from a single city, stops in each of the other cities just once, and then returns to the beginning location. The goal of the problem is to determine the salesman's shortest path from a specific city while minimizing the overall cost. Concepts of fuzzy sets are now widely employed to simulate real-world situations with intrinsic uncertainty and imprecision, such assignment problems and TSP. It is frequently thought that transit time between nodes in conventional TSP solutions depends only on distance. Journey times are actually greatly impacted by variables like traffic and road conditions. To address these limitations, we propose a novel approach to solving the Travelling Salesman Problem (TSP) using pentagonal fuzzy numbers. We demonstrated our proposed algorithm with a numerical example and provide a comparative analysis with an existing algorithm.