In many practical situations, we need to know how uncertainty propagates through data processing algorithms, i.e., how the uncertainty in the inputs affects the results of data processing. This problem is important for all types of uncertainty: probabilistic, interval, and fuzzy. From the computational viewpoint, however, this problem is much more complex for interval and fuzzy uncertainty. Therefore, for these types of uncertainty, it is desirable to design faster algorithms.
In this paper, we describe faster algorithms for two practically important situations:
linearization situations, when the approximation errors are small and therefore, the data processing algorithms can be replaced by a linear function, and
monotonic situations, when the dependence of the result y of data processing on each of the inputs x1, ..., xn is either monotonically increasing or monotonically decreasing.