Subject: Fuzzy relations vs. Mamdani model
From: Andrej Albert (firstname.lastname@example.org)
Date: Fri Nov 10 2000 - 14:19:40 MET
I am a Ph. D student and I am trying to find an answer to the
Originally a fuzzy rule "if A, then B" was defined to be seen as a
fuzzy relation between the input A and the output B. The
compositional rule of inference was used to calculate the output for
an input value A'. This meant to calculate the intersection between
the cylidrical extension of A and the fuzzy set of the relation and
then to project the resulting fuzzy set onto the domain of B.
The Mamdani/Assilian model for fuzzy systems, however,
calculates the degree of compatibility of the input A' with A then
uses the minimum for implication which cuts the fuzzy set B and
My question now is: are these two methods equivalent or is the
second one a simplified model of the first one? Is a solution of the
Mamdani model for multiple rules one but not the smallest solution
of the system of relational equations? Or is the Mamdani model
only valid for crisp input values?
Thank you very much for any help!
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