Re: Fuzzy sets theory

Scott Dick (dick@morden.csee.usf.edu)
Thu, 21 May 1998 13:45:25 +0200 (MET DST)

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Probably your best bet would be to read a good general textbook on fuzzy
set theory. There's a good one by George Klir and Bo Yuan called "Fuzzy
Sets and Fuzzy Logic: Theory and Applications." It contains a good answer
to your question about t-norms.

Hope this helps!

Andrzej Pownuk wrote:

> Probably may question are very naive, I apologize for that.
>
> This are my questions:
>
> 1) How to construct a membership functions?
> Does exist any objective methods or experiment?
>
> I know paper:
> Civanlar M.R., Trussell H.J.,
> Constructing Membership Functions Using Statistical Data.
> Fuzzy Sets and Systems. Vol. 18, 1986.
>
> 2) Let A={a1/x1, a2/x2}, B={b1/y1, b2/x2} are two fuzzy sets.
> C=A U B={max(a1,a2)/x1, max(a1,a2)/x2} etc.
>
> Why?
>
> I know about t-norms but why t-norms?
> I can invent many similar functions.
>
> (e.g. C=AUB={|cos(a1^a2+453*a1)|/x1, |sin(a2*a2)|/x2 }
> (I know sum of Yager, Dubois and Prade, Dombi etc.)
>
> Does exist any experiment which verify fuzzy calculation?
>
> I have read some books
>
> (e.g. Yager R.R., Essentials of fuzzy modeling and control.
> John Wiley & Sons 1994.
> Onisawa T., Kacprzyk J.,
> Reliability and Safety Analyses
> under Fuzziness.
> Physica-Verlag Heidelberg 1995,
> Kai-Yuan Cai, Introduction to fuzzy reliability.
> Kluwer Academic Publishers London 1996 etc.)
>
> and many articles about fuzzy sets theory.
> I have listened lectures of prof. Czogala and prof. Zadeh (only 1 hour)
> but I still do not know answer to this question.
>
> Thanks in advance.
>
> Andrzej Pownuk
>
> --------------------------------------------------------
> MSc. Andrzej Pownuk
> Silesian Technical University
> Faculty of Civil Engineering
> Chair of Theoretical Mechanics
> Ul. Krzywoustego 7, 44-100
> Gliwice, POLAND
> Tel/fax ++48-32/371542
> URL: http://zeus.polsl.gliwice.pl/~pownuk
> E-mail: pownuk@zeus.polsl.gliwice.pl.
> --------------------------------------------------------

--
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*                               *                                     *
*  Scott Dick                   *                                     *
*  Research Assistant           *       Cool & brilliant thought      *
*  USF Computer Science         *       still under contruction       *
*  dick@morden.csee.usf.edu     *                                     *
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Probably your best bet would be to read a good general textbook on fuzzy set theory. There's a good one by George Klir and Bo Yuan called "Fuzzy Sets and Fuzzy Logic: Theory and Applications." It contains a good answer to your question about t-norms.

Hope this helps!
 

Andrzej Pownuk wrote:

Probably may question are very naive, I apologize for that.

This are my questions:

1) How to construct a membership functions?
Does exist any objective methods or experiment?

I know paper:
Civanlar M.R., Trussell H.J.,
Constructing Membership Functions Using Statistical Data.
Fuzzy Sets and Systems. Vol. 18, 1986.

2) Let A={a1/x1, a2/x2}, B={b1/y1, b2/x2} are two fuzzy sets.
C=A U B={max(a1,a2)/x1, max(a1,a2)/x2} etc.

Why?

I know about t-norms but why t-norms?
I can invent many similar functions.

(e.g. C=AUB={|cos(a1^a2+453*a1)|/x1, |sin(a2*a2)|/x2   }
(I know sum of Yager, Dubois and Prade, Dombi etc.)

Does exist any experiment which verify fuzzy calculation?

I have read some books

(e.g. Yager R.R., Essentials of fuzzy modeling and control.
         John Wiley & Sons 1994.
         Onisawa T., Kacprzyk J.,
         Reliability and Safety Analyses
         under Fuzziness.
         Physica-Verlag Heidelberg 1995,
         Kai-Yuan Cai, Introduction to fuzzy reliability.
         Kluwer Academic Publishers London 1996  etc.)

and many articles about fuzzy sets theory.
I have listened lectures of prof. Czogala and prof. Zadeh (only 1 hour)
but I still do not know answer to this question.

      Thanks in advance.

                     Andrzej Pownuk

--------------------------------------------------------
MSc. Andrzej Pownuk
Silesian Technical University
Faculty of Civil Engineering
Chair of Theoretical Mechanics
Ul. Krzywoustego 7, 44-100
Gliwice, POLAND
Tel/fax ++48-32/371542
URL: http://zeus.polsl.gliwice.pl/~pownuk
E-mail: pownuk@zeus.polsl.gliwice.pl.
--------------------------------------------------------

 
-- 
***********************************************************************
*                               *                                     *
*  Scott Dick                   *                                     *
*  Research Assistant           *       Cool & brilliant thought      *         
*  USF Computer Science         *       still under contruction       *
*  dick@morden.csee.usf.edu     *                                     *
*                               *                                     *
***********************************************************************
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