In the context of risk analysis and decision analysis, uncertainty is usually formulated using probability, although occasionally something like fuzzy arithmetic will be used.
Empirical quantities used as input for risk and decision analysis may have uncertainty arising from many sources. Here are a few, as categorized by M. Granger Morgan and Max Henrion1:
The importance of this list is that different types of uncertainty need to be recognized and treated in different ways. For example, statistical variation is usually described with a probability distribution. Variability, however, may entail a probability distribution of another probability distribution, which becomes messy quickly.
1Morgan, M. Granger, and Henrion, Max. Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policay Analysis, Cambridge University Press, 1990.