>In response to John Watkins, (sorry I didn't receive your reply):
Most people call me Fred.
>If you represent a single input, single output system using fuzzy logic then
>you will get an output which simply reproduces your fuzzy rule set unless there
>are input values for which there are no explicit rules, in which case the
>output will depend on the rules and the shape of the fuzzy sets used to
>represent the knowledge within the network.
Come again? I can reproduce a bounded SISO system *exactly* with just
one or two rules. Guaranteed. You might want to rethink your claim.
>The power of the fuzzy paradigm, whether you use liguistic or crisp inputs and
>outputs, lies in the inference (generalisation) that occurs if your rule base
>is incomplete and you choose the fuzzy set shapes correctly.
What some call generalization others call interpolation. And that "if"
about choosing the fuzzy sets correctly is a big one sometimes. But I
wasn't debating the power of the technique; I was inquiring how one
might implement a "linguistic" system. If with numbers, I indicated,
one might as well not bother with the words.
>You are correct to say that with three distinct inputs and three rules which
>don't interfere with each other, then the output can only take one of three
>values.
With only three distinct inputs (words) there are only three output
values possible, regardless, interference or no. The outputs can be
numbers or fuzzy sets or whatever, but there can be no more than
three. First and last, a fuzzy system is a FUNCTION.
>If your network had four inputs of three values each then the output
>(conceptually) can take 3**4 (to the power of) values, and to completely
>describe the network would require the same number of rules. A fuzzy system can
>be used to infer an output with an order of magnitude fewer rules and can then
>represent the output in the form Low/Medium/High, or 55, or however you choose
>to interpret it.
Agreed, under your conditions a saturated rulebase would have 3^4
rules. Where didi you get this "order of magnitude" business? I think
you'll be hard pressed to justify that remark for the general case.
It's not a matter of individual interpretation about the output. It'll
be numeric or not. And if not, what? Words? There'll never be enough.
Words and numbers? Then why not just use numbers? THAT's my point.