Abstarct: Finding the shortest path in a graph is one of important problems in graph theory.. This problem can be applied in transportation, routing, communication and so on. In the real application of shortest path problem the arc length may represent time or cost which is not a real number. In this case it is applicable to utilize fuzzy numbers. In this thesis we consider the fuzzy shortest path problem where the arc lengths are fuzzy numbers. Two algorithms are considered and compared for solving this problem. We also consider the multi-criteria fuzzy decision-making problem.