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In this study, we introduce a Fuzzy Time-Dependent Network (FTDN) and analyze its shortest path problem. The FTDN is a network in which travel times are represented as fuzzy sets and are also time-dependent. Under these circumstances, the shortest path problem on the FTDN is far more complex in comparison with the shortest path problem on the existing networks. To highlight the complexity, we show that on the FTDN, "standard" shortest path algorithms (e.g., the well-known Dijkstra algorithm) are not able to come up with solutions. Subsequently, we construct a suitable method which is suitable to deal with the shortest problem. A fuzzy programming model is presented for finding the shortest path on the FTDN. The proposed model is handled through the techniques which combine mechanisms of fuzzy simulation and genetic optimization. In this particular setting, fuzzy simulation is exploited to estimate the value of uncertain functions, which do not exist in the general networks. The proposed model is evaluated with the use of numerical experimentation. A comparative analysis demonstrates that the proposed model leads to the shortest path while standard algorithms are not capable of finding the path when dealing with the shortest path problem on the FTDN.