Solving Travelling Salesman Problem Using Dynamic Programming Under Extended Fuzzy Environment

The main intention of this article is to solve travelling salesman problem (TSP) under an extended fuzzy environment. Uncertainty of a TSP can occur due to factors like variable travel duration, unpredictable road conditions, etc. In this article, these uncertainties are handled using intuitionistic and interval-valued intuitionistic fuzzy parameters. Moreover, the dynamic programming technique is applied to get the best optimal solution. In addition, numerical examples are formulated that contain cost parameters that are triangular intuitionistic fuzzy numbers and interval-valued intuitionistic fuzzy numbers, and solved by the proposed method. The results of the proposed dynamic approach are compared with existing algorithms, including brute- force and branch and bound methods.