# Re: Basic Theory

From: Yasser (bdm@microbrains.net)
Date: Tue Mar 27 2001 - 23:47:38 MET DST

• Next message: Nico du Bois: "Rough fuzzy sets, fuzzy rough sets ;-)"

"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
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