methods for approximate reasoning

Subject: methods for approximate reasoning
albert@massivbau.tu-darmstadt.de
Date: Tue Nov 14 2000 - 08:41:55 MET

Hi everybody!

I have a (maybe very simple) question for which I cannot find an
answer in any reference.
Originally fuzzy rules have been defined to be fuzzy relations
between the input A and the output B. The result for a (fuzzy or
crisp) input is calculated by applying the compositional rule of
inference, i.e. by intersecting the cylindrical extension of an input
value A' with the fuzzy set of the relation and then projecting the
resulting fuzzy set onto the domain of B.
Most fuzzy systems use models which appear to be different. They
first calculate the degree of compatibility of the input values with
the fuzzy sets on the left hand side of the fuzzy rule. Then they
aggregate the degrees of compatibility (e.g. using the min-
operator). Using an implication operator (e.g. again min) they
calculate the result of the rule and then they accumulate the
results to get one fuzzy result of the rule set. Finally a crisp value
is obtained using a defuzzification method.
My question is: are these two methods equal for both crisp and
fuzzy input parameters? Or is the second one a simplification of
the original one?

Thanks for any help!
Andrej
**********************************
Dipl.-Ing. Andrej Albert
Institut für Massivbau
TU Darmstadt
Alexanderstraße 35
Tel.: 06151/16-7036
Fax : 06151/16-7034
*********************************

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