Re: Membership functions.

Earl Cox (ecox@metus.com)
Wed, 16 Jun 1999 16:22:17 +0200 (MET DST)

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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>
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