Re: number of membership functions?

Robert Land (101665.216@compuserve.com)
Sun, 7 Jun 1998 02:33:11 +0200 (MET DST)

Jonathan & Hasan,
could you explain what 'membership functions' are? I'm programming part of
a Project based on a book written by 'Dipl.-Ing D. Traeger, ISBN
3-519-16162-1'. The book is in German, so I might have come across MFs, but
cannot realy translate their sense.

Regards,

Robert Land
_______________________________________

Jonathan G Campbell wrote:

> 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?
> >
> [...]
>
> 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 that one aspect of the 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. Of course, I'm speaking only for numerically
> trained systems.
>
> 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 JG.Campbell@ulst.ac.uk http://www.infm.ulst.ac.uk/~jgc/

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