CONCLUSIONS AND RECOMMENDATIONS - Modelling Uncertainty in Flood Forecasting Systems - page 136

7.1.6 Expert judgement-based method and Qualitative Uncertainty Scales
The expert judgement-based qualitative method for uncertainty assessment (Subsection
3.2.2) is applied to the flood forecasting model of River Loire. Given the qualitative as-
sessments of the parameter uncertainty by the experts (with respect to quality and impor-
tance of the parameters), this method allows for the estimation of the uncertainty due to
all recognisable sources without a significant increase in computation time. Although this
method has the same mathematical structure as that of the FOSM method (Subsection 3.4.2),
the evaluations of the quality and importance (similar to the variance and sensitivity, respective-
ly, of the FOSM method) are fully based on expert judgement. Consequently, it is a very
approximate and rather holistic method. Therefore, in flood forecasting, this method should
be used only as a complement to the quantitative methods like MC, FOSM and EP,
particularly to obtain some indication of the relative effects of some of the sources of un-
certainty, which cannot be incorporated into the framework of the quantitative methods.
Also of importance is the way in which the results of this method are interpreted. Sun-
dararajan (1994 & 1998) attempted to interpret the results of this method by
comparing it with the results from the probabilistic method using the so-called
benchmarking values. The information contained by the results of such a qualitative
method may be better communicated if they are interpreted qualitatively. Therefore, in
the course of this research, the Qualitative Uncertainty Scales were developed (Section
4.3) with which the results can be measured qualitatively.
7.1.7 Probability-possibility transformation and hybrid technique for
uncertainty modelling
A hybrid technique of uncertainty modelling is defined as a method that makes use of
both probabilistic and possibilistic or fuzzy approaches together. There are at least two
types of situations where the hybrid technique can be useful. These situations are
referred to in this thesis as Type I and Type II Problems. The Type I Problem is the situa-
tion where an uncertain variable possesses components from both randomness and fuzzi-
ness. The Type II Problem refers to the situation where there exists some parameters with
enough data to characterise their uncertainty using probability distributions and some other
uncertain parameters with very little or no data to characterise their uncertainty in
a probabilistic manner. This latter set of parameters can be more suitably characterised
for uncertainty by means of the possibilistic approach using fuzzy membership
functions. This then gives rise to a system with two sets of uncertain parameters: one rep-
resented by probability distributions and the other represented by membership functions.
The major obstacle in modelling uncertainty of a system of Type II Problem comes
from the differences of operation between random-random (R-R) and fuzzy-fuzzy (F-F)
variables. Part of this research is also devoted to explore the differences and similarities
in the operations between R-R and F-F variables, and to investigate a probability-
possibility (or fuzzy) transformation that takes these differences into account. This
research shows that the addition and multiplication of two fuzzy variables by the EP
using the ! -cut method is similar to corresponding operations between two functionally
dependent random variables for some specific conditions. The transformations also
provide an alternative method for the evaluation of the Extension Principle for a