Environmental Engineering Reference
In-Depth Information
(UK). Finally, we provide some discussion and
conclusions.
Although theymay give accurate predictions, they
provide little or no insight into the underlying
nature of the system being modelled. Further-
more, it is difficult to identify a transparent set
of conditions that result in a particular prediction.
This makes it difficult to trace and examine the
basis for decisions informed by tools that incor-
porate black-boxmethods. In this chapter we shall
instead focus on the application of rule-based
methods to flood forecasting. These rules incor-
porate linguistic descriptions of values in the form
of fuzzy labels and also allow for the explicit
representation of probabilistic uncertainty.
Hence, for a particular prediction they enable us
to identify a set of fuzzy mappings fromwhich the
prediction is generated. In summary, wewillmake
the case that AI methods based on fuzzy-probabi-
listic rules can potentially provide an effective and
transparent tool for flood forecasting.
In the next section we introduce Label Seman-
tics, an integrated theory of fuzziness and proba-
bility. Following this we describe two fuzzy
learning algorithms, Linguistic Decision Trees
and Fuzzy Bayes. The next two sections present
case studies of applications in flood forecasting:
the first shows how linguistic decision trees can
be used to classify regions of weather radar
images so as to aid in Bright Band detection;
the second introduces a number of problems in-
volving time-seriesmodelling including flow fore-
casting for the Bird Creek catchment (USA) and
level prediction for the Upper Severn catchment
Integrating Fuzzy and Probabilistic
Uncertainty
Both uncertainty and fuzziness are inherent to the
complex systems associated with flood forecast-
ing. The former results from natural random pro-
cesses, from model incompleteness and from a
lack of information about important parameters
and measurements. The latter is a consequence of
imprecision and noise in data measurements in-
cluding river levels, river flow, rainfall etc. Label
semantics has been introduced by Lawry (2006) as
an uncertainty theory for fuzzy description labels,
which allows for an integrated treatment of both
types of uncertainty within a coherent unified
framework.
In label semantics a continuous universe
V
is
partitioned using a finite set of labels LA (e.g.
possible labels include low, medium, high, about
20, etc.). Each label L is defined by an appropriate-
nessmeasure
m
L
:
V!½
0; 1
where for x
Þ
is the subjective probability that label L is an
appropriate label to describe x. Figure 8.1 shows
trapezoidal appropriateness measures for labels
L
1
,
...
, L
n
. In this case each label describes a closed
interval of the real line together with a neighbour-
ing region, with decreasing appropriateness as
distance from the core interval increases.
2 V m
L
ð
x
...
L
1
L
2
L
3
L
4
L
5
L
n
Fig. 8.1
Fuzzy labels defined by trapezoidal appropriateness measures.
