Environmental Engineering Reference
In-Depth Information
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Uncertain input data: gaps, inaccuracy, spatial and temporal variability, hetero-
geneity, qualitative ecosystem attributes
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Uncertain input-output relationships: complex systems, non-linear interactions,
management of multiple variables, exceptions to general rules, different impor-
tance of variables
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Uncertain output: qualitative classes, non-ordinal classes, non-sharp boundaries
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Uncertain expert knowledge, legislative requirements, opinions of administra-
tors, end-users, etc, expressed in linguistic form
Fuzzy models of ecosystem functions have been developed in all continents,
confirming that the principles of fuzzy logic theory have been established worldwide
in ecological institutions. Fuzzy systems have been developed for air, water, soil
ecosystems, with both biotic and abiotic ecosystem variables. Analysis and assess-
ment of air pollution, water eutrophication, groundwater contamination, control of
ozone levels, evaluation of sustainability of fishery and fish farming, analytical
assessment of soil degradation, leaching or acidification risk, are just a few examples
of ecological issues modelled with a fuzzy approach that can be found in the scientific
literature.
In a number of cases, fuzzy logic has also been combined with GIS or with other
soft computing techniques, such as artificial neural networks, self-organizing maps,
and genetic algorithms in order to integrate the adaptability of fuzzy logic to human
reasoning with a data-driven approach.
Most authors have acknowledged that fuzzy logic represents a suitable, feasible and
effective tool to deal with ecological issues, and that it provides more reliable results
when compared with other methods for environmental assessment (e.g. Altunkaynak
et al. 2005). Fuzzy logic has demonstrated to be particularly suitable for the develop-
ment of new indices of ecological quality. It allows one to acknowledge the subjective
aspects of the index design process, and provides the tools to easily handle subjectivity,
by quantifying it and manipulating it with mathematical rigour (Table
10.1
).
10.2 Structure of a Fuzzy Model
A fuzzy model typically consists of three stages: fuzzification, inference and
defuzzification. The latter is not always required.
Fuzzification is the process for linking a variable to its underlying characteristics
by means of a membership function
. After fuzzification, the input variable loses
its numerical definition and acquires a linguistic definition: for example, it might
become
small, hot, high
. Its numerical value is transformed into a fuzzy member-
ship grade: a unit-less number in the interval [0, 1].
Once all variables are fuzzified, they can be processed through the fuzzy rules of
the model. This is the inference stage. Fuzzy rules typically are in the form of
logical implication (
if ... then
). Single rules are then combined to produce a fuzzy
output, still in the form of fuzzy membership grade in the [0, 1] interval.
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