Re: Selecting membership functions

rshepard@xxxxxxxxxxxxxxxxxxxxxx wrote:
On 2007-07-30, Kirk Zurell <kirk@xxxxxxxxxxxxx> wrote:

2. Triangular and trapezoid functions offer partial degrees of truth, so
these offer the real meat of fuzzy calculations. If your input can be
somewhat x and somewhat y at the same time, choose these. If in doubt,
choose these.

Such linguistic variables are much better represented by smooth curves
such as the Gaussian (normal curve, bell curve) with S- and Z-shape curves
at the ends of the domains. The semantics are that the rate of change of the
truth values (membership degree, mu) varies as the domain value varies and
that there is a gradual approach and departure from the maximum truth value.
In the world of subjective decision making (unlike in fuzzy control
applications) these are both more realistic and easier for people to accept
than are trapezoids and triangles.

Thanks for adding this. Working almost exclusively in control,
we're aware of the use of smooth curves but have never used them
ourselves (not yet, anyway). OP might need these more than the
triangles/trapezoids: Inferjack didn't mention his intended
application.

Kirk

--
Kirk Zurell
Byte Craft Limited
Waterloo, Ontario, Canada
http://www.bytecraft.com
.

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