Fuzzy sets theory

Andrzej Pownuk (pownuk@zeus.polsl.gliwice.pl)
Mon, 18 May 1998 03:56:43 +0200 (MET DST)

Probably my 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 System, Vol. 18, 1986 pp. 1-13.

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.


I know about t-norms but why t-norms?
I can invent many similar functions.
(I know sum of Yager, Dubois and Prade, Dombi etc.

Does exist any experiment which verify fuzzy calculation?
I have read some books

Yager R.R., Filev D.P., Essentials of Fuzzy Modeling and Control.
John Wiley & Sons 1994.
Kai-Yuan Cai, Introduction to Fuzzy Reliability. Kluwer Academic Publishers,
London 1996
Onisava Takehisa, Kacprzyk Janusz, Reliability and Safety Analyses under
Physica-Verlag Heildelberg 1995)

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.