The paper proposes a novel approach to designing the algorithms for prognostics of gas distribution networks (GDNs) and preventing the possible emergencies. The main idea is based on transforming the accumulated data which characterize the behavior of the network informative parameters to the framework of interval-valued time series. Such a model supposes that the history of the parameter change is represented by the intervals of its values at a number of discrete time points. The obtained description allows taking the uncertainty into account and forecasting the GDN state for the best and the worst scenarios. The case of GDN has some peculiarities caused by periodicity (seasonality) of gas demands. For finding proper forecasts under those conditions, the `interval'-based version of Holt-Winters' algorithm also known as triple exponential smoothing is developed. The effectiveness of the proposed approach is analyzed to identify an area of its applicability and formulate the practical recommendations.