CONTRIBUTION OF PRESENT RESEARCH TO UNCERTAINTY ASSESSMENT METHODS - Modelling Uncertainty in Flood Forecasting Systems - page 79

Figure 4.18. Uncertainty in the output Q in the form of a CDF: one obtained
directly from random simulation (by modified MC simulation) and
the other transformed from a MF, which is obtained from fuzzy
simulation (by EP).
Figure 4.19. Uncertainty in the output Q in the form of a MF: one obtained
directly from fuzzy simulation (by EP) and the other transformed
from a CDF, which is obtained from random simulation (by modified
MC simulation).
4.4.5 Concluding remarks
It is proved here that the addition and multiplication of two fuzzy variables by the
Extension Principle using ! -cut is similar to corresponding operations between two
functionally dependent random variables for some specific conditions. The dependency
should be such that the sum and the product are monotonically increasing. This means
that the addition and multiplication operations on such random variables can be