Environmental Engineering Reference
In-Depth Information
by Lotfi A. Zadeh, is a soft computing approach particularly suitable for ecological
models.
Fuzzy logic is an alternative method to represent complex systems, such as those
encountered in biology, sociology or economy. Instead of numerical variables and
mathematical formulas, fuzzy models require linguistic variables and rules. For
example: the variable
temperature
might have linguistic values such as
hot
or its
antonym c
old
; a linguistic rule might be: “
if
pressure is
high
,
then
volume is
low
”.
This approach helps ecologists who have an idea of the process under study, but have
data affected by too much imprecision to be used in the development of a formal
model. Fuzzy logic applies meaning to imprecise concepts and uses uncertainty as an
additional source of information. The first key concept of fuzzy logic is partial truth.
Rather than labeling a statement as either
true
(1) or
false
(0), as classic binary logic
does, in fuzzy logic the degree of truth of a statement can assume any value between
0 and 1. The degree of truth is established by a membership function
.Membership
functions, the second key concept, represent the transition from numbers to words
and allow one to “compute with words”. Dealing with fuzziness and imprecision does
not prevent fuzzy logic from being a mathematical formalism, and fuzzy systems
being sound and not ambiguous. Bart Kosko, one of the pioneers in the development
of fuzzy systems, demonstrated that “
an additive fuzzy system can uniformly approx-
imate any real continuous function on a compact domain to any degree of accuracy
”
(Kosko 1994).
Fuzzy logic has had a great impact on mathematical disciplines such as logic,
algebra, topology, data analysis, etc. Technical applications include a variety of
different controllers and software, for example: chips that control cameras, eleva-
tors, air conditioners, washing machines and other home appliances; automobile
and other vehicle subsystems, such as automatic transmissions, ABS and cruise
control; artificial intelligence in video games; edge detection in digital image
processing; pattern recognition algorithms in remote sensing; and language filters
for offensive text in message boards and chat rooms. The impact of fuzzy logic on
ecological research has displayed an increasing trend: the first applications date
from the late 1980s, when it was introduced for the ordination of vegetation data.
Since then, more than two hundred publications about fuzzy applications in eco-
logical research have appeared in scientific journals.
m
10.1.2 Fuzzy Logic and Ecology
Fuzzy logic has been repeatedly proposed as a powerful technique to develop
models for decision support
in ecosystem management (Silvert
1997
,
2000
;
Adriaenssens et al.
2004
;Fr
anzle 2006; Jørgensen 2008). The capability of fuzzy
logic to use uncertain information that other methods cannot take into account
makes this computational technique particularly important in ecology. In fact, the
representation of ecosystems is affected by many sources of fuzziness:
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