The article describes a method for solving the fuzzy traveling salesman problem on a given transportation network based on a two-stage approach. In the fuzzy traveling salesman problem, the task is to find the shortest route with a fuzzy specified travel time between individual cities of the network. The travel time along the network is given in the form of fuzzy trapezoid numbers. A method for converting fuzzy numbers into a special form is proposed, and operations on such numbers are considered. The route is formed in two stages: at the first stage, the cities of the network are grouped into clusters, after which the optimal solution to the traveling salesman problem is found for each cluster using a genetic algorithm. A modification of the genetic algorithm scheme is used based on improving the mutation operation and increasing the diversity of populations. Two variants of the cluster formation topology with a limited number of available paths and a fully connected topology are considered. Numerous experiments are conducted, the results of which confirm the constructiveness of using the preliminary clustering methodology for a large number of cities in the network. Pre-clustering improves the overall route duration in the traveling salesman problem compared to solutions obtained by using a genetic algorithm without using clusters.