CONTRIBUTION OF PRESENT RESEARCH TO UNCERTAINTY ASSESSMENT METHODS - Modelling Uncertainty in Flood Forecasting Systems - page 70

In the EP, on the other hand, there is no provision (with the present state-of-the-art) for
the treatment of correlations between variables. The EP, however, can be greatly
simplified if the function is monotonic.
These differences can be illustrated by taking a simple example of the addition of two
independent random variables defined by uniform PDFs and two fuzzy variables defined
by constant MFs (Schulz and Huwe, 1997). As shown in Figure 4.13, the summation of
two uniformly distributed independent random variables results in a triangular
distribution, whereas the sum of two fuzzy variables with constant MFs results in a
constant MF (Fig. 4.14).
In essence, the operation on fuzzy variables by the EP is a deterministic method
whereas the operation on random variables by the MC method is non-deterministic. As
illustrated later in this section, if two variables are functionally dependent on each other,
in certain cases the operation on the random variables also happens to be deterministic.
In which case operations on random variables and on fuzzy variables with monotonic
functions are similar.
Figure 4.13. Summation of two independent random variables with uniform
PDFs (derived by the Monte Carlo method).