Environmental Engineering Reference
In-Depth Information
Table 10.1 The fuzzy approach can be useful in different ways to develop an ecological index.
A number of issues that can be encountered in the process of index development is presented, with
the respective solutions offered by the fuzzy approach
Issues of the index development process
Solutions
Boundaries
Many “traditional” indices subdivide the
range of a variable into intervals
associated with different scores or quality
classes. Boundaries between two intervals
are often sharp. In this way, small
deviations from a threshold value implies
big differences in the output. This is not in
agreement with the behaviour of natural
systems
Fuzzy membership functions allow to
represent soft boundaries and
gradients. Membership functions can
overlap: a variable value can display
two characteristics at the same time
System complexity
One of the most desirable features of
ecological indices is the ability to combine
metrics in a manner that is complex
enough to capture the dynamics of
essential ecological processes, but not so
complex that their meaning is obscured
(Borja and Dauer 2008)
Fuzzy rule-based systems are able to
model non-linear, multidimensional,
complex phenomena; yet, the
linguistic form of the if ... then rules
make fuzzy models easily
understandable
Reference conditions
Reference conditions, required to define the
class of best ecological quality, should be
described by pristine, undisturbed
environments. Unfortunately, such
conditions may not exist anymore.
Scientists are thus required to define
virtual reference conditions using
mathematical models and/or expert
judgement
Fuzzy models are mathematical models,
based on logic rules, and are also
expert systems, based on expert
judgement
Legislative criteria
Classes of ecological quality (e.g. good,
moderate, poor ) do not have a clear
quantitative definition. Threshold values
that separate two quality classes should
take into account the levels of
acceptability and public concern, which
are highly subjective, and not directly
measurable
Fuzzy membership functions are suitable
for representing purely linguistic
variables, such as classes of ecological
quality. They could be designed with
some degree of overlap, avoiding hard
thresholds and integrating different
conceptions of good or poor ecological
quality
Defuzzification is the process to convert the fuzzy output into a non-fuzzy value
that can be used in non-fuzzy contexts.
The following subsections will present an overview of the most used techni-
ques for fuzzification, inference and defuzzification. In fact, the three stages can
be performed in many different ways (Table 10.2 ), depending on the type of
information integrated in the model and on the required output. This plasticity is an
Search WWH ::




Custom Search