EXISTING MATHEMATICAL METHODS FOR UNCERTAINTY ASSESSMENT - Modelling Uncertainty in Flood Forecasting Systems - page 34

Figure 3.3. Membership functions of linguistic variables: (a) Quality and (b)
Importance .

Derivation of parameters from sub-parameters
A parameter may be decomposed into several sub-parameters. In this case the importance
is evaluated for the parameter, but the quality is assessed individually for the sub-
parameters. The reason is that the quality of a parameter depends on the qualities of its
sub-parameters, which may vary depending on the situations or events. It should be noted
that the importance can also be derived from the importance of subparameters applying
the similar procedure as for the quality. But care should be taken that the evaluated
importance of the sub-parameter is for its contribution to the importance of its parameter
not to the total uncertainty. The quality of the parameter can be derived by weighting the
qualities of its sub-parameters represented by fuzzy numbers as given in Equation (3.22).

(3.22)

( i =1,…, n s ) is the quality of the

where " is the quality of a given parameter;
subparameter i, n s is the number of sub-parameters, and w i is the crisp weight of the i th
sub-parameter. The symbol (+) represents the addition between fuzzy numbers. The
weights satisfy the following property:

(3.23)