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monotonic function without using the ! -cut method. It appears that the direct implication
of this finding is very limited, but it is certainly an important basis for further research
into probability-possibility transformations and hybrid techniques of uncertainty
modelling.
7.2 Recommendations for further research and development
7.2.1 Uncertainty assessment should be an integral component of flood
forecasting systems
Despite the fact that the presence of uncertainty in flood forecasting is significant, the
implementation of uncertainty analysis in operational real time flood forecasting is very
limited. As long as forecasts are subject to uncertainty the only honest and sensible way
is to admit it and to incorporate this information in decision making as much as possible.
Hiding it creates the illusion of certainty, the consequences of which could be very large.
Therefore, it is essential that all forecasting systems should have an uncertainty
assessment procedure as an integral component.
7.2.2 Probabilistic and possibilistic approaches should b\e considered
as complementary
The founder of fuzzy set theory, L.A.Zadeh himself, suggested that probabilistic and
possibilistic approaches should be considered as complementary and NOT competitive
(Zadeh, 1995). A similar view was reported by several other researchers, e.g. Kikuchi
and Pursula (1998). The present author also believes that these two theories should be
viewed as complementary. If this view is realised by the researchers and practitioners of
uncertainty modelling, the art of uncertainty representation and modelling will certainly benefit.
7.2.3 Towards hybrid techniques of uncertainty modelling
The hybrid technique of uncertainty modelling, whereby the combined application of the
probabilistic and possibilistic or fuzzy approaches is sought, has been discussed by
several researchers. The fact that both the probabilistic and fuzzy set approaches have
some limitations in representing and modelling uncertainty, it can be argued that the
analysis of the uncertainty can be best handled using a combination of probabilistic and
fuzzy approaches. Such a hybrid technique may have an advantage in incorporating both
randomness and vagueness types of uncertainty explicitly. Therefore, to obtain the
benefit from both the probability and fuzzy techniques, the research on the hybrid
technique of modelling uncertainty should be explored further.
In some situations of uncertainty/risk-based decision making, for example for flood
warning, the application of the hybrid technique may be appropriate. The risk-based
decision-making requires that the risks be evaluated for different decision alternatives. In
probabilistic sense, risk is defined as the probability of occurrence of an (future) event
times the consequence of the event. In the context of flood warnings, the future event is
 
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