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Table 1: Results of all fuzzy approaches to the global
temperature change problem.
Method MSE #Rules Time
ANFIS 2.38% 27 15sec.
TSK-IRL-R 3.03% 50 50min.
MOGUL-TSK-R 3.09% 121 >60min.
MOGUL-IRLHC-R 10.08% 34 28min.
FIR 0.25% 56 5sec.
Therefore, it can be concluded that the different
fuzzy approaches used to model the global
temperature change problem are useful for the task
at hand, because all of them have a high level of
prediction accuracy. Depending on the users
interests it can be more desirable to choose a
methodology with high precision in the prediction,
like FIR, or a less precise model but with a small
number of rules in it, like ANFIS, MOGUL-IRLHC-
R or TSK-IRL-R.
This work is an initial attempt to compare
different types of fuzzy modeling approaches when
dealing with ecological systems. It does not pretend,
at this point, to be an exhaustive and rigorous
comparison, but to give a first inside into hybrid
fuzzy modeling of ecological problems. The next
step is to incorporate other fuzzy-based
methodologies, such is the LR-FIR, which is an
attempt to reduce the number of FIR rules obtained
while minimizing the loss of precision in the
prediction. Finally, we plan to study other ecological
problems mainly focused in climate systems.
5 CONCLUSIONS
This paper studies the usefulness of hybrid fuzzy
modelling approaches when dealing with a real
ecological system, i.e. the global temperature
change. A box model of the ocean-atmosphere, that
reproduces satisfactorily the wide range of
temperature increase reported by the IPCC, is used.
From the temperature increase calculated with
the box model, different hybrid fuzzy models are
built. Concretely, the ANFIS that is a neuro-fuzzy
system, the TSK-IRL-R, MOGUL-TSK-R and
MOGUL-IRLHC-R that are genetic-fuzzy systems
based on the iterative rule learning approach, and the
FIR methodology. All the models are able to predict
accurately the global temperature increase in the
year 2100. The fuzzy models presented in this paper
are simpler than the box model and are much more
understandable from a policy maker point of view.
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