Re: number of membership functions?

Jonathan G Campbell (
Thu, 21 May 1998 19:33:13 +0200 (MET DST)

Hasan R. Haznedaroglu wrote:
> 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: [cut]

I'm shooting from the hip here, so I'm probably ignoring a large
literature on the subject. I have done some superficial empirical
analysis and it seems the real problem may be the same as that of bin
size in histograms. If you go for high resolution in the fuzzy
partition, the number of (training) data per cell/set reduces --
eventually to zero.

Look up the literature on probability density estimation, particularly
Parzel kernels. Also Probabilistic Neural Nets are closely related to
Parzen kernel density estimation.

References on request.

Best regards,

Jon Campbell

Jonathan G Campbell Univ. Ulster Magee College Derry BT48 7JL N. Ireland 
+44 1504 375367