CONTRIBUTION OF PRESENT RESEARCH TO UNCERTAINTY ASSESSMENT METHODS - Modelling Uncertainty in Flood Forecasting Systems - page 66

(4.36)
(4.37)
where
(4.38)
(4.39)
The scales derived using Equations (4.34) through (4.39) are in fuzzy scales because the
regions of different uncertainty levels are represented by fuzzy variables. The fuzzy
scales are transformed to crisp scales such that the boundaries between the two scales are
non-fuzzy. In this transformation from fuzzy to crisp scales, the abscissa passing through
the point of intersection of two consecutive levels on fuzzy scales separates the two
consecutive levels on the crisp scales. An example of fuzzy and crisp scales is shown in
Figure 4.9. The QUS in this example consist of five divisions: Very Small Uncertainty
(VSU), Small Uncertainty (SU), Moderate Uncertainty (MU), Large Uncertainty (LU)
and Very Large Uncertainty (VLU). The VSU and VLU correspond to the best- and
worst-case scenarios, respectively. In the figure, the boundaries of fuzzy scales are
shown in thin-dark and thick-grey lines and the boundaries of crisp scales in thick-dark
vertical lines. Note that the QUS varies case to case. The scales shown here is for the
example presented in Subsection 4.3.2.
Figure 4.9. An example of fuzzy and crisp qualitative scales. The fuzzy scales
are represented in thin-dark and thick-grey lines and the crisp scales
are represented in thick-dark likes.