**Subject: **Fuzzy relations vs. Mamdani model

**From: **Andrej Albert (*albert@massivbau.tu-darmstadt.de*)

**Date: **Fri Nov 10 2000 - 14:19:40 MET

**sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephan Lehmke: "CFP: 7th Fuzzy Days, Dortmund, Germany, Oct 1-3, 01"**Previous message:**Larry Hall: "IFSA/NAFIPS 2001 Final call for papers"**Next in thread:**albert@massivbau.tu-darmstadt.de: "Fuzzy relations vs. Mamdani model"**Next in thread:**Ulrich Bodenhofer: "Re: Fuzzy relations vs. Mamdani model"**Reply:**Ulrich Bodenhofer: "Re: Fuzzy relations vs. Mamdani model"

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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**Next message:**Stephan Lehmke: "CFP: 7th Fuzzy Days, Dortmund, Germany, Oct 1-3, 01"**Previous message:**Larry Hall: "IFSA/NAFIPS 2001 Final call for papers"**Next in thread:**albert@massivbau.tu-darmstadt.de: "Fuzzy relations vs. Mamdani model"**Next in thread:**Ulrich Bodenhofer: "Re: Fuzzy relations vs. Mamdani model"**Reply:**Ulrich Bodenhofer: "Re: Fuzzy relations vs. Mamdani model"

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