The aim of the Traveling Salesman Problem (TSP) is to find the cheapest way of visiting all elements in a given set of cities (nodes) exactly once and returning to the starting point. In solutions presented in the literature costs of travel between nodes are based on Euclidean distances, the problem is symmetric and the costs are constant and crisp values. Practical application in road transportation and supply chains are often uncertain or fuzzy. The risk attitude depends on the features of the given operation. The model presented in this paper handles the fuzzy, time dependent nature of the TSP and also gives a solution for the asymmetric loss aversion by embedding the risk attitude into the fitness function of the eugenic bacterial memetic algorithm. Computational results are presented for different cases. The classical TSP is investigated along with a modified instance where some costs between the cities are described with fuzzy numbers. Two different techniques are proposed to evaluate the uncertainties in the fuzzy cost values. The time dependent version of the fuzzy TSP is also investigated and simulation experiences are presented. © 2011.