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"AlanMcRob" <alanmcrob@aol.com> wrote in message

news:20010324213723.01436.00000539@ng-de1.aol.com...

*> Can anyone explain the basic theory behind fuzzy logic to me.
*

Basically, fuzzy logic is about the fuzziness of logic. Meaning that in

real life, things are not always black or white, true or false, etc. They

actually come in various "grey levels". For example, there is a tall man

and a short man, but is a 175 cm man short or tall? The answer is fuzzy. He

is tall compared to a 150 cm man, but short compared to a basket ball

player. It all depends on the context and perception.

In logic, we deal with "sets". For example, the set of numbers {1,2,3}.

Now any number can either belong to that set (eg. number 2) or does not

belong to that set (e.g. number 4). This is called "crisp" logic and has

been in use for thousands of years. Now, consider the set of all tall men.

Does a 175 cm man belong to this set or not? The answer depends on what you

mean by "tall men", it is vague, it is fuzzy.

Hence, fuzzy logic is the logic that deals with situations where you can't

give a clear yes/no type of answer. This turns out to be a very common

situation in many human decision making processes. It also has significant

applications for systems that are highly non-linear and very complex to

model mathematically.

In Zadeh's fuzzy logic, the gradual transition from Yes to No, True to

False, is expressed by a "membership function", graphically describing the

degree of truth of a certain proposition. Crisp logic is thus just a

special case of fuzzy logic. In crisp logic, membership functions are just

one vertical line, whereas in fuzzy logic, they have a distribution. For

practical purposes, you can think of membership functions like probability

distributions (although conceptually, there is a difference).

Once, you accept this "membership function" issue, the rest is just standard

logic operation (AND, OR, NOT, UNION, INTERSECTION, etc) and standard

arithmetic ( +, -, x, etc), only that these operations have been extended to

include the effect of membership functions. This turns out to be handy in

many practical situations, for example: automatic control. Why spend time

solving complex non-linear equations, and testing stability etc, when you

can achieve the same commercial outcome by means of few "fuzzy rules"?

Conceptually, fuzzy logic is a nice new idea; mathematically, it is

revolutionary; commercially it means more money for your product. However,

to be fair, the outcome you get from FL is always achievable by other means.

In my opinion, Fuzzy logic, Neural Networks, Genetic Algorithms,

Probability, Fractals, etc are all faces of the same daemon: a unifying

piece of science yet to be discovered.

Finally, Fuzzy Logic seems to be in contradiction with all mono-theistic

religions including Christianity, and in good conformity with Buddhism.

That is why half the Fuzzy Logic population is in China.

-- Yasser Ali Mechanical Engineering Dept., J07 Sydney University############################################################################ 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:**Nico du Bois: "Rough fuzzy sets, fuzzy rough sets ;-)"**Previous message:**Brian M. Schott: "Re: Syntactical Rule"**Next in thread:**Paul Victor Birke: "Re: Basic Theory"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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