number of membership functions...

Hasan R. Haznedaroglu (hasanh@coes.LaTech.edu)
Thu, 21 May 1998 13:27:37 +0200 (MET DST)

I am still struggling to find answers to some basic
questions about fuzzy logic (after writing a related
thesis!). I would appreciate any answer--if not, any
comment you might have after reading the following
questions.

My first question:

I remember reading a passage about the number of
membership functions (MFs) that should be used
(or recommended) during fuzzy reasoning, 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