**Previous message:**Wolfgang von Hansen: "Software for fuzzy computation"**Next in thread:**Fenri: "Re: Basic Theory"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

Yasser wrote:

*>
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*> "AlanMcRob" <alanmcrob@aol.com> wrote in message
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*> news:20010324213723.01436.00000539@ng-de1.aol.com...
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*> > Can anyone explain the basic theory behind fuzzy logic to me.
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*>
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*> Basically, fuzzy logic is about the fuzziness of logic. Meaning that in
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*> real life, things are not always black or white, true or false, etc. They
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*> actually come in various "grey levels". For example, there is a tall man
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*> and a short man, but is a 175 cm man short or tall? The answer is fuzzy. He
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*> is tall compared to a 150 cm man, but short compared to a basket ball
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*> player. It all depends on the context and perception.
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*>
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*> In logic, we deal with "sets". For example, the set of numbers {1,2,3}.
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*> Now any number can either belong to that set (eg. number 2) or does not
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*> belong to that set (e.g. number 4). This is called "crisp" logic and has
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*> been in use for thousands of years. Now, consider the set of all tall men.
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*> Does a 175 cm man belong to this set or not? The answer depends on what you
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*> mean by "tall men", it is vague, it is fuzzy.
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*>
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*> Hence, fuzzy logic is the logic that deals with situations where you can't
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*> give a clear yes/no type of answer. This turns out to be a very common
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*> situation in many human decision making processes. It also has significant
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*> applications for systems that are highly non-linear and very complex to
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*> model mathematically.
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*>
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*> In Zadeh's fuzzy logic, the gradual transition from Yes to No, True to
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*> False, is expressed by a "membership function", graphically describing the
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*> degree of truth of a certain proposition. Crisp logic is thus just a
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*> special case of fuzzy logic. In crisp logic, membership functions are just
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*> one vertical line, whereas in fuzzy logic, they have a distribution. For
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*> practical purposes, you can think of membership functions like probability
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*> distributions (although conceptually, there is a difference).
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*>
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*> Once, you accept this "membership function" issue, the rest is just standard
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*> logic operation (AND, OR, NOT, UNION, INTERSECTION, etc) and standard
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*> arithmetic ( +, -, x, etc), only that these operations have been extended to
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*> include the effect of membership functions. This turns out to be handy in
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*> many practical situations, for example: automatic control. Why spend time
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*> solving complex non-linear equations, and testing stability etc, when you
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*> can achieve the same commercial outcome by means of few "fuzzy rules"?
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*>
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*> Conceptually, fuzzy logic is a nice new idea; mathematically, it is
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*> revolutionary; commercially it means more money for your product. However,
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*> to be fair, the outcome you get from FL is always achievable by other means.
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*> In my opinion, Fuzzy logic, Neural Networks, Genetic Algorithms,
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*> Probability, Fractals, etc are all faces of the same daemon: a unifying
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*> piece of science yet to be discovered.
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*>
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*> Finally, Fuzzy Logic seems to be in contradiction with all mono-theistic
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*> religions including Christianity, and in good conformity with Buddhism.
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*> That is why half the Fuzzy Logic population is in China.
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*> --
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*> Yasser Ali
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*> Mechanical Engineering Dept., J07
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*> Sydney University
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************************************

Dear Yasser

This was a wonderfully concise yet full explanation!

Only to add by saying the membership function itself, by this I mean its

special shape we hold so dear, usually is somekind of "S" shape,

normally symetric but not necessarily so I have claimed its form could

be generally in 3-parameter Weibull in shape. I mean the "S" shape

would correspond to the CDF of a Weibull PDF Distribution with variable

to the modeller the full SCALE, SLOPE & __LOCATION__ parameters!

Paul

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