Dhouib-Matrix-TSP1 Method to Optimize Octagonal Fuzzy Travelling Salesman Problem Using α-Cut Technique (International Journal of Computer and Information Technology(2279-0764), 2021)
This paper proposes the optimization of the fuzzy travel salesman problem by using the α-Cut technique as a ranking function and the Dhouib-Matrix-TSP1 as an approximation method. This method is enhanced by the standard deviation metric and obtains a minimal tour in fuzzy environment where all parameters are octagonal fuzzy numbers.Fuzzy numbers are converted into a crisp number thanks to the ranking function α-Cut. The proposed approach in details is discussed and illustrated by a numerical example. This method helps in designing successfully the tour to a salesman on navigation through the distance matrix so that it minimizes the total fuzzy distance.
Keywords: Optimization; Fuzzy Numbers; Travelling Salesman Problem; Approximation Method; Ranking Function; α-Cut Technique