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

*WSiler@aol.com*

**Date: **Tue Nov 14 2000 - 17:47:30 MET

**sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Masoud Nikravesh: "BISC: BISC Seminar; Nov 21-2000: Adaptive Agent Oriented Software Architecture (AAOSA)"**Previous message:**Masoud Nikravesh: "BISC: 1st ANNOUNCEMENT"**Maybe in reply to:**albert@massivbau.tu-darmstadt.de: "Fuzzy relations vs. Mamdani model"**Next in thread:**Jon Williams: "Re: Fuzzy relations vs. Mamdani model"**Maybe reply:**WSiler@aol.com: "Re: Fuzzy relations vs. Mamdani model"

In a message dated 11/14/00 1:37:53 AM Central Standard Time,

albert@massivbau.tu-darmstadt.de writes:

<< 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? >>

I think this question was answered a couple of days ago, qbut since it is an

important question I answer it again.

Actually, the fuzzy relation involved a fuzzy implication operator, and is

completely unworkable for any true fuzzy implication operator (one which

collapses to the classical implication for crisp values). However, an

unspoken non-aggression pact among fuzzy mathematicians meant that nobody

called attention to this embarassing fact. The Mamdani "implication" operator

works, but since it does not collapase to the classical for crisp values it

is not an implication operator at all. Unfortunately I do not know of a

thorough discussion of this point in the literature, although Klir and Yuan

give a correct although brief discussion of the Mamdani method.

Almost all the theoretical literature assumes that a rule is a fuzzy logical

proposition. In fact, a rule in any working system is not a fuzzy logical

proposition; instead, the antecedent is a fuzzy logical proposition, and the

consequent is a set of instructions to be executed with the combined

antecedent and rule confidence if the antecedent is sufficiently true. In

executing the consequent we must have a convention for handling any prior

truth values of data to be modified by the rule. Those who actually construct

fuzzy expert system shells and systems face several theoretical problems

here, which (again unfortunately) almost no fuzzy theoreticians have

addressed.

William Siler

############################################################################

This message was posted through the fuzzy mailing list.

(1) To subscribe to this mailing list, send a message body of

"SUB FUZZY-MAIL myFirstName mySurname" to listproc@dbai.tuwien.ac.at

(2) To unsubscribe from this mailing list, send a message body of

"UNSUB FUZZY-MAIL" or "UNSUB FUZZY-MAIL yoursubscription@email.address.com"

to listproc@dbai.tuwien.ac.at

(3) To reach the human who maintains the list, send mail to

fuzzy-owner@dbai.tuwien.ac.at

(4) WWW access and other information on Fuzzy Sets and Logic see

http://www.dbai.tuwien.ac.at/ftp/mlowner/fuzzy-mail.info

(5) WWW archive: http://www.dbai.tuwien.ac.at/marchives/fuzzy-mail/index.html

**Next message:**Masoud Nikravesh: "BISC: BISC Seminar; Nov 21-2000: Adaptive Agent Oriented Software Architecture (AAOSA)"**Previous message:**Masoud Nikravesh: "BISC: 1st ANNOUNCEMENT"**Maybe in reply to:**albert@massivbau.tu-darmstadt.de: "Fuzzy relations vs. Mamdani model"**Next in thread:**Jon Williams: "Re: Fuzzy relations vs. Mamdani model"**Maybe reply:**WSiler@aol.com: "Re: Fuzzy relations vs. Mamdani model"

*
This archive was generated by hypermail 2b25
: Tue Nov 14 2000 - 18:15:24 MET
*