Re: Fuzzy relations vs. Mamdani model


Subject: Re: Fuzzy relations vs. Mamdani model
From: Iris Gilsdorf (iris.gilsdorf@mch20.sbs.de)
Date: Sun Nov 19 2000 - 22:15:06 MET


Hallo,

I think it will be a help to read
Driankov, Hellendoorn, Reinfrank
An Introduction to Fuzzy Control
ISBN 3-540-606912
page 85 ff. ( Representing the Meaning of IF-then Rules )
There you can find an answer and perhaps more questions ..

Iris

Andrej Albert wrote:
>
> Hi!
>
> I am a Ph. D student and I am trying to find an answer to the
> following question:
> 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
> so on...
> 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!
>
> Best regards
> Andrej
>
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