Re: fuzzy logic

["Craig Carey <research@ijs.co.nz>" <research@ijs.co.nz>]

On Tue, 23 Aug 2005 17:45:49 +0200, "Dmitry A. Kazakov" wrote:
>On 23 Aug 2005 06:23:18 -0700, Craig Carey <research@ijs.co.nz> wrote:
>> On Tue, 16 Aug 2005 15:03:41 +0200, "Dmitry A. Kazakov" wrote:
>>>On Tue, 16 Aug 2005 13:46:37 +0200, Poul-Erik Andreasen wrote:
>>>> ...source-code examples of the use of Dmitry A. Kazakov's  fuzzy-logic
>>>> library?.
>> ...
>>>P.S. If that is not directly related to Ada, then comp.ai.fuzzy is a better
>>>place to discuss it. Or write me (E-mail is on the page.)
>>
>> A tall rectangle can fit inside of a smaller square, providing that the
...

(Purpose) Please, no more ANN messages on fuzzy logic, at this
Usenet group.

>Do you mean fuzzy numbers or something else?.

Anything. There can be two forms for 0.7:
(1) a plain 1-D polytope of 1st order classical logic: (0<=R<=0.7)
(2) the fuzzy logic scalar, 0.7 (a point with a magnitude).

With the 2nd option, simplifying expressions becomes a problem.
Mr Kazakov's software doesn't handle unevaluated symbolic
expressions. With such simplicity, there would tend to be
no discovery that fuzzy logic theory is faulty.

...
>I presume you meant and = min, or = max.

That statement corrects my statement.

>> This:
>>
>>    4 and (2*(0<x) or 3*(0<y));
>
>This is a rather flawed notation that mixes values and sets. What is 4?

There was not a use of sets.
The number "4" is a point polytope.
"*" can mean "and" since "*" and "Min" happen to give the same result.

...
>I cannot tell if I understood the question,

I didn't have a question. I aim to stop the ANN-on-fuzzy-logic
e-mails that comp.lang.ada has gotten, in the past.

...
>Yes, but it has nothing to do with fuzzy logic. Reasoning about geometric
>shapes is crisp as long as the predicates involved are crisp.

Such a trivial program....
Better would be to have the user supply multiplication tables.

>See above. Fuzzy logic has any sense only if 1) the data you are working
>with or 2) the knowledge of what's going on are incomplete, contradictory
>etc.

  http://www.dmitry-kazakov.de/ada/fuzzy.htm

You missed something.
There could be new "error" value, defined so that all outputs
are the error value, if an input has that value. (A competitor to
the 'raise' statement).

...
>Yet note that on each step of reasoning, each answer a feasible fuzzy
>system gives is *correct*. It might end up with "I don't know", but it
>cannot derive falsehood from truth.

If it gets any worse then it would be AI-302-ish:
 trivial, arbitrary, unlikely to be used, probably appealing to
 AdaCore but to increase the chance of a reponse, e-mail can be
 routed via programmers in France.

Lukasiewicz (Poland) had a 3-valued logic (0, 0.5, 1) (that seems to
have been ignored).

...
>2. Are the laws fuzzy?
>= somebody was too lazy to take a look into a handbook of elementary
>mathematics.

So fuzzy logic seems analogous to RISC versus CISC, and CISC (i.e.
classical logic) seems better.

If you read books then does the logic of Zadeh allow the number to
take a value bigger than 1.0?:
 Reference:  L. A. Zadeh, "Fuzzy Sets", Information and Control,
  1965, Vol 8, pp 338-353.



Craig Carey
Auckland