Environmental Engineering Reference
In-Depth Information
Table 10.2 Stages of a fuzzy model and some possible options for developing each step
Model stages
Steps requiring definition
by the model developer
Possible options
Definition can be
Fuzzification
Input variables
Qualitative or quantitative
Knowledge-driven
(ecological
knowledge)
Membership functions:
number
Generally 2-5
Knowledge-driven
or data-driven
Membership functions:
position along the
x -axis
Depends on the variable
range; generally in
[0, + 1 ],
or [-
Knowledge-driven
or data-driven
1
,+
1
]
Membership functions:
shape
Linear (triangular,
trapezoidal), or non-
linear (gaussian,
sigmoidal, others)
Knowledge-driven
or data-driven
Inference
Model type
Takagi-Sugeno or
Mamdani
Knowledge-driven
if ... then rules
Depend on the problem
Knowledge-driven
or data-driven
Mathematical operators
Min and max; product,
weighted sum, others
Knowledge-driven
or data-driven
Weights (optional)
Any positive real number
Knowledge-driven
or data-driven
Defuzzification
(optional)
Type of output
Qualitative or quantitative
Knowledge-driven
Defuzzification method
Centroid, mean, max, mean
of maximum, center of
maximum, bisector,
linear combination,
“winner takes all”,
others
Knowledge-driven
or data-driven
important feature of the fuzzy approach, which allows one to deal with any kind of
data. On the other hand, the variety of choices that exist at each stage may be seen
as a difficulty and a source of subjectivity: ecologists have no guidelines to select
the most opportune techniques for a specific problem. The definition of several
steps listed in Table 10.2 can be data-driven, i.e. based on statistical evaluation of
data sets or machine learning techniques. Optimal parameterization of member-
ship functions, weights, rules, etc., is recommended as it improves model perfor-
mance, but it is only possible when an adequate amount of experimental data is
available. Unfortunately, in ecological research it is often difficult to collect large
data sets, especially when biological information (populations, communities) is
involved. Therefore, the knowledge-driven approach, based on expert opinion, is
the most common strategy to define membership functions and if ... then rules
in ecological fuzzy models. Of course, it introduces more subjectivity into the
model.
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