In many practical situations, inputs to a data processing algorithm are known with interval uncertainty, and we need to propagate this uncertainty through the algorithm, i.e., estimate the uncertainty of the result of data processing. Traditional interval computation techniques provide guaranteed estimates, but from the practical viewpoint, these bounds are too pessimistic: they take into account highly improbable worst-case situations when all the measurement and estimation errors happen to be strongly correlated. In this paper, we show that a natural idea of having more realistic estimates leads to the use of so-called interactive addition of intervals, techniques that has already been successful used to process interval uncertainty. Thus, we provide a new justification for these techniques. If we use a known interpretation of a fuzzy set as a nested family of intervals -- its alpha-cuts -- then we can naturally extend our results to the case is fuzzy uncertainty.