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.

Why?

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

(e.g.
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
Fuzziness.
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

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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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