The Time Dependent Traveling Salesman Problem (TD TSP) is an extension of the classic Traveling Salesman Problem towards more realistic conditions. TSP is one of the most extensively studied NP-complete graph search problems. In TD TSP, the edges are assigned different weights, depending on whether they are traveled in the traffic jam regions (such as busy city centers) and during rush hour periods, or not. In such circumstances, edges are assigned higher costs, expressed by a multiplying factor. In this paper, we introduce a novel and even more realistic approach, the Interval Intuitionistic Fuzzy Time Dependent Traveling Salesman Problem (IVIFTD TSP); which is a further extension of the classic TD TSP, with the additional notion of deploying interval valued intuitionistic fuzzy for describing uncertainties. The core concept employs interval valued intuitionistic fuzzy sets for quantifying the traffic jam regions, and the rush hour periods loss (those are additional costs of the travel between nodes), which are always uncertain in real life. Since type-2 (such as inter valued) fuzzy sets have the potential to provide better performance in modeling problems with higher uncertainties than the traditional fuzzy set, the new approach it may be considered as an extended, practically more applicable, extended version of the original abstract problem. The optimization of such a complex model is obviously very difficult; it is a mathematically intractable problem. However, the Discrete Bacterial Memetic Evolutionary Algorithm proposed earlier by the authors' team has shown sufficient efficiency, general applicability for similar type problems and good predictability in terms of problem size, thus it is applied for the optimization of the concrete instances.