So let's go back to the picture which we have discussed as a prototype application before.

If you have such a thing, even with 234 rules inside it, the question always is, do I have

enough rules?

Do I have even more rules inside there?

And the answer is, you never have a final answer to this.

You might not be aware about all the possible rules, which means, is there any chance to

check if your rule system is complete?

And the funny point is, yes, there is a chance to do so.

And how do you do it?

Well, the question is, the raw information that I have,

that are the numbers down side here in the input layer.

And we have our FASES stuff giving you an output.

And the question now is, are there more information

in the raw inputs here, which I have not squeezed out

by the rule system?

And to check this, let's take the answer coming

from the rule system, put it to final output, which

has the same target values as here.

But then in parallel to this FASES story here,

neural FASES story there, let's add a new feedforward neural

network, which directly sees the data

and then does a data analysis to reduce the residual error, which

is not in the first place explained by the FASES system.

There in this example here, you see an extended architecture

there.

And if there would be more information in the inputs,

which I haven't covered by my rule system,

then you would expect that at least in the training set,

my result should be better than in the FASES system alone.

So first of all, you do your FASES neural FASES system here.

Then you have to reside from the neural FASES system here.

And all the other stuff here is deactivated.

And then you activate it, which means

you forward the information of the FASES output

here to the final output.

And so if you check the output versus target here,

then there would be only a small residual error,

which has to be explained away by this feedforward neural

network here on this side.

And the answer to this exercise in our example

here is that you see practically no difference.

See, on the return of invest curve here,

you see extreme small changes in the curve

here at some local positions here.

But overall, that's practically no difference

what's coming from the FASES system

and our FASES system and the overall system

with the combined feedforward neural network in addition.

Also here in the generalization, so practically you

see the same curves once again, which