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 * * * * * ***********************************************************************
--------------B7F12F0994AAA5005BB84766 Content-Type: text/html; charset=us-ascii Content-Transfer-Encoding: 7bit
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 * * * * * ***********************************************************************--------------B7F12F0994AAA5005BB84766--