The aim of the traveling salesman problem (TSP) is to find the cheapest way of visiting all elements in a given set of cities and returning to the starting point. In solutions presented in the literature costs of travel between nodes (cities) 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 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 solution for the asymmetric loss aversion by embedding the risk attitude into the fitness function of the bacterial memetic algorithm. Computational results are presented as well. © 2010 Springer-Verlag.