understanding neural nets

[David Cary]

goetz at zoesis.com (Phil Goetz) allegedly said:
...
>Fuzzy logic isn't the same sort of thing as a neural network.
>A neural network performs computation.  Fuzzy logic is a set of rules
>for performing logical operations with fuzzy set membership.
>
>First you define a fuzzy set membership function.
>In Zadeh's original paper, this was a function that had a big middle area
>where its value was 1, and triangular areas at each end where the membership
>value decayed linearly to 0 in each direction.  If you have some parameter
>to tell you whether something falls within some range, you specify the min,
>min certain, max certain, and max, so that f(min) = 0 = f(max),
>f(min_certain) = 1 = f(max_certain), interpolating linearly.
...
>Ta-da!  Fuzzy logic.  That's all there is to it.
>
>So the phrase "mathematically equivalent fuzzy logic representation of
>a neural network" doesn't make sense.
>
>
>Phil goetz at zoesis.com

Correct me if I'm wrong here, but I thought that a single neuron (in most
NN simulations) had a nonlinear function so that its output approximates
zero for "low" input values, some sort of ramp for middling values, and one
for "high" input values. To me, this looks similar to one of Zadeh's
"membership functions" that has "max_certain" and "max" set to +infinity.
(Every set of membership functions I've ever seen has had at least one
'degenerate' function like this, one with "max_certain" and "max" set to
+infinity). (Many neural networks use this exact same flat-straight-flat
function).

Given a single-layer perceptron with N outputs (using simple
flat-straight-flat neurons), I think I can generate a set of N fuzzy logic
membership functions, translating the NN "weights" to the FL min, max, and
certain regions.
Then, if you give these 2 systems the same numeric input, they both give
identical numeric outputs.

Since multiple layers of a neural network are connected differently than
the layers of rules in a fuzzy system, you are right in saying that they
are not identical. Still, they seem so tantalyzingly similar.

Is there anything that neural networks *are* mathematically identical to ?

--
David Cary "mailto:d.cary at ieee.org" "http://www.rdrop.com/~cary/"
"icbmto:N36 08.830' W97 03.443'"
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