Re: Membership functions.

Pramit 'Jake' Sarma (psarma@che.iitb.ernet.in)
Fri, 25 Jun 1999 10:45:58 +0200 (MET DST)

That is certainly a correct way of re-interpreting what I meant by
observing the fuzzy surface. We all have 'biases' in the point of view,
and that is one of the reasons for the fuzzy map shaping I mentioned. I am
'biased' in the sense of approach to fuzzy logic by essentially using it
for the control of nonlinear dynamical systems. In control, input/output
maps are vital intermediate tools, and given the complexity of Fuzzy Logic
Control (FLC) systems this is a good way to get an a priori handle on the
FLC, the goal of the FLC design being high-quality [finally crisp]
control. In the FLC design the fuzzy logical semantics gets suppressed, and
the standard approach is to treat the FLC as a multiparameter tweakable
block. The way of looking at things is often dependent on the thing
itself, in Fuzzy Logic just as it is in Nature.

Pramit

On Wed, 16 Jun 1999, Earl Cox wrote:

> You should not be surprised that changing the shape of a knowledge base's
> fuzzy sets changes the output control surface of the rules. After all, it is
> the fuzzy sets that specify the semantics of the rule. If you change the
> shape of a fuzzy set, you change the semantics of the knowledge. The fact
> that the organizational framework -- the rules -- remain the same is
> immaterial. When you change the topology (or, more properly, the morphology)
> of the fuzzy sets, you change the way the collection of rules behave, you
> change how truth membership grades are transferred, and you change how the
> solution control surface is constructed.
>
> A very simple expert system shows this. Consider a weight estimating system
> of one fuzzy rule,
>
> if height is Tall then weight is Heavy
>
> where Tall is a linear increasing fuzzy set and weight is a right-facing
> S-curve. Running this rule will give us an estimate of weight. If you now
> change the shape of Tall to a skewed S-curve, you will get a very different
> weight estimate. In fact, without changing the rule, you can generate many
> different weight estimating models simply by changing the fuzzy set shapes.
>
> Just a comment.
> Earl
>
>
> Pramit 'Jake' Sarma wrote in message ...
> >A very useful experimental way to check the 'goodness' of MF geometry is
> >by inspecting the input/output surface generated by the fuzzy
> >inferencer with a given rule-base. There can be striking differences in
> >the surface for different MF shapes for the *identical* rule-base.
> >
> >On Fri, 4 Jun 1999, yucel kok wrote:
> >
> >>
> >> Ioannis Dokas heeft geschreven in bericht
> >> <374c7967.6715120@news.otenet.gr>...
> >> >I' m searching for various ways in order to determine memberships
> >> >functions based on experamental values. Olso I' m looking for
> >> >criterias consening selecting the best mebership functions for several
> >> >cases.
> >> >
> >> >
> >> >Anyone with referenses?
> >> >THANKS
> >>
> >> Neuro-fuzzy system can determine the mf's of fuzzy rules. Search NEFPROX

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Pramit "Jake" Sarma
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e-mail: jake_n_jazz@yahoo.com e-mail: psarma@che.iitb.ernet.in

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