Fuzzy Measures in Inductive Reasoning
Abstract
Inductive Reasoning is a technique which allows us to reason about a finite
state representation of a system on the basis of available data. If the data
stem from a continuous system, they are first discretized (recoded) into a
finite set of discrete values. Recently, optimal recoding techniques have been
devised which are presented in this paper. The forecasting power of the
Inductive Reasoning approach has been shown to be dramatic in a number of
examples. Yet, the forecast was always expressed in terms of the recoded, i.e.
the discrete, variables, and not in terms of the original continuous variables.
Recently, we have been working on a modification of the technique which allows
us to reconstruct the continuous signals from the forecast discrete signals with
very good accuracy. For this purpose, we exchanged the previously used
probabilistic quality measures for fuzzy quality measures, and we predict,
together with the discrete states also new fuzzy membership functions of the
forecast signals. From these membership functions, we can then regenerate the
continuous signals. The technique has been tested by means of a third order
continuous-time linear system and has given promising results. These results
are presented here.
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Last modified: June 22, 2005 -- © François Cellier