Allocating efficient routes to taxiing aircraft, known as the Ground Movement problem, is increasingly important as air traffic levels continue to increase. If taxiways cannot be reliably traversed quickly, aircraft can miss valuable assigned slots at the runway or can waste fuel waiting for other aircraft to clear. Efficient algorithms for this problem have been proposed, but little work has considered the uncertainties inherent in the domain. This paper proposes an adaptive Mamdani fuzzy rule based system to estimate taxi times and their uncertainties. Furthermore, the existing Quickest Path Problem with Time Windows (QPPTW) algorithm is adapted to use fuzzy taxi time estimates. Experiments with simulated taxi movements at Manchester Airport, the third-busiest in the UK, show the new approach produces routes that are more robust, reducing delays due to uncertain taxi times by 10–20% over the original QPPTW.