ADV MATH SCI JOURNAL Advances in Mathematics: Scientific Journal 9 (2020), no.11, 9417–9427 ISSN: 1857-8365 (printed); 1857-8438 (electronic) https://doi.org/10.37418/amsj.9.11.46 IMPROVED HUNGARIAN METHOD TO SOLVE FUZZY ASSIGNMENT PROBLEM AND FUZZY TRAVELING SALESMAN PROBLEM S. DHANASEKAR 1 , V. PARTHIBAN, AND A. DAVID MAXIM GURURAJ ABSTRACT. In this paper an improved Hungarian method is introduced for solv- ing fuzzy assignment problem. When we apply Hungarian method to solve fuzzy assignment problem, if the minimum number of lines crossing the fuzzy zeros are not equal to the order of the fuzzy cost matrix, this method can be used to get the optimal solution with less computational work. This method reduces the computational work of getting the optimal solution. Further this method can also be applied for finding the Hamiltonian circuit with minimum fuzzy cost in the fuzzy traveling salesman problem. Some numerical examples are furnished to understand the algorithm. 1. I NTRODUCTION Assignment problem deducted from a transportation problem by imposing some additional constraints. It is to find one to one mapping from machines to jobs with the objective that the assignment cost is least. To obtain the optimum assignment, several approaches have been proposed. Hungarian method is the most acclaimed method for solving assignment problem. Kuhn [1] proposed this method and named it as Hungarian method since it is developed from the works of the two Hungarian mathematicians D Konig and Egerváry. Further Munkers [2] gave structure for algorithm. Travelling Salesman problem is to 1 corresponding author 2020 Mathematics Subject Classification. 90C08, 90C70, 90B06, 90C29, 90C90. Key words and phrases. Fuzzy number, Triangular fuzzy number, Trapezoidal fuzzy number, Fuzzy arithmetic operations, Fuzzy Assignment Problem, Fuzzy traveling salesman problem. 9417