**Subject: **methods for approximate reasoning

*albert@massivbau.tu-darmstadt.de*

**Date: **Tue Nov 14 2000 - 08:41:55 MET

**sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Bernard De Baets: "Announcement EUROFUSE 2001"**Previous message:**albert@massivbau.tu-darmstadt.de: "Fuzzy relations vs. Mamdani model"**Next in thread:**Pim van den Broek: "Re: methods for approximate reasoning"**Reply:**Pim van den Broek: "Re: methods for approximate reasoning"

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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**Next message:**Bernard De Baets: "Announcement EUROFUSE 2001"**Previous message:**albert@massivbau.tu-darmstadt.de: "Fuzzy relations vs. Mamdani model"**Next in thread:**Pim van den Broek: "Re: methods for approximate reasoning"**Reply:**Pim van den Broek: "Re: methods for approximate reasoning"

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