number of membership functions?

Hasan R. Haznedaroglu (hasanh@coes.LaTech.edu)
Mon, 18 May 1998 03:49:38 +0200 (MET DST)

My first question:

I remember reading a passage about the number of
membership functions (MFs) that should be (or recommended)
used in a fuzzy system, in Constantin von Altrock's book.
The recommended number was about (if I'm not wrong) 7 for
each variable. The reason for using such a low number was
that humans can use only few linguistic terms simultaneously
during their reasoning or decision making processes.

Wouldn't using more MFs increase the precision of the fuzzy
system? Suppose we are provided with sufficient amount of
(training) data to generate a rule-base that could cover
tens(or hundreds) of MFs. Then why limit ourselves with few MFs?

Second question:

Fuzzy logic is always referred as the technique which can deal
with linguistic uncertainties. That's why the MFs are represented
by linguistic terms. This makes it easy to incorporate linguistic
rules obtained from a human expert.

However, in cases where only numerical data is used to generate
rules, is it still necessary to label each MF by a linguistic term?

What if a large number (say 50) of MFs is used? Wouldn't it
be inconvenient to use a separate linguistic term for each MF?
Could "numbers" instead of linguistic terms be used? In that case
a fuzzy rule would look like:
(x1,x2)-->(y):
If x1 is "13" and x2 is "35" then y is "46"

Thanks...

Hasan

If we use tens(or hundreds) of MFs then how

why are membership functions represented by
linguistic terms