This paper presents two new types of fuzzy shortest-path network problems. We consider the edge weight of the network as uncertain, which means that it is either imprecise or unknown. Thus, the first type of fuzzy shortest-path problem uses triangular fuzzy numbers for the imprecise problem. The second type uses level (1 - b, 1 - a) interval-valued fuzzy numbers, which are based on past statistical data corresponding to the confidence intervals of the edge weights for the unknown problem. The main results obtained from this study are: (1) using triangular fuzzy numbers and a signed distance ranking method to obtain Theorem 1, and (2) using level (1 - b, 1 - a) interval-valued fuzzy numbers, combining statistics with fuzzy sets and a signed distance ranking method to obtain Theorem 2. We conclude that the shortest paths in the fuzzy sense obtained from Theorems 1 and 2 correspond to the actual paths in the network, and the fuzzy shortest-path problem is an extension of the crisp case.