Dealing with uncertainty in fuzzy inductive reasoning methodology
  The aim of this research is to develop a reasoning under uncertainty strategy
in the context of the Fuzzy Inductive Reasoning (FIR) methodology. FIR emerged
from the General Systems Problem Solving developed by G. Klir. It is a data
driven methodology based on systems behavior rather than on structural
knowledge. It is a very useful tool for both the modeling and the prediction of
those systems for which no previous structural knowledge is available. FIR
reasoning is based on pattern rules synthesized from the available data. The
size of the pattern rule base can be very large making the prediction process
quite difficult. In order to reduce the size of the pattern rule base, it is
possible to automatically extract classical Sugeno fuzzy rules starting from
the set of pattern rules. The Sugeno rule base preserves pattern rules
knowledge as much as possible. In this process some information is lost but
robustness is considerably increased. In the forecasting process either the
pattern rule base or the Sugeno fuzzy rule base can be used. The first option
is desirable when the computational resources make it possible to deal with the
overall pattern rule base or when the extracted fuzzy rules are not accurate
enough due to uncertainty associated to the original data. In the second
option, the prediction process is done by means of the classical Sugeno
inference system. If the amount of uncertainty associated to the data is small,
the predictions obtained using the Sugeno fuzzy rule base will be very
accurate. In this paper a mixed pattern/fuzzy rules strategy is proposed to
deal with uncertainty in such a way that the best of both perspectives is used.
Areas in the data space with a higher level of uncertainty are identified by
means of the so-called error models. The prediction process in these areas
makes use of a mixed pattern/fuzzy rules scheme, whereas areas identified with
a lower level of uncertainty only use the Sugeno fuzzy rule base. The proposed
strategy is applied to a real biomedical system, i.e., the central nervous
system control of the cardiovascular system.
