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Rich Ulrich <wpilib@pitt.edu> wrote in message

news:<o4elntgdqdr1vb0gvtt7ng3leeraqp723m@4ax.com>...

*> On Wed, 15 Aug 2001 05:50:46 GMT, "Earl Cox" <earldcox1@home.com>
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*> wrote:
*

(( cuts ))

*>
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*> Smithson's book gave me the impression of disparate
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*> researchers, different models of "fuzzy logic," and a field
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*> that was not unified to any great extent. A decade
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*> later, is that different?
*

Earl certainly refers to "fuzzy logic" in a way that would disregard

what I and other researchers have contributed. Where all fuzzy

researchers necessarily agree is that there exist terms in natural

language with membership or characteristic function over a relevant

domain such that some points in the domain have membership strictly

between 0 and 1: there are degrees of membership. That is what

fuzziness means. And that is where agreement pretty much ends.

For the very basic concept of what operationally is this notion of

degree of membership, and how to measure it, there is disagreement.

And indeed, that is what started this thread. I take the view that

fuzzy membership is really a form of semantic likelihood, a notion

which explains in pretty straightforward terms what fuzziness is

(st least in natural language semantics), and how it arises, given

that even in calibrational settings, there is randomness in usage.

The next point of disagreement relates to the choice of rules for

connectives. Earl appears to champion the min-max rules. And the

fact that these rules fail to obey law of excluded middle (LEM), and

law of contradiction (LC) is trumpeted often as a virtue, and it

is implied that fuzziness in itself *requires* that LEM and LC must

fail.

Here again, I for one disagree. I maintain that natural language

fuzziness is not sufficient to cause LEM and LC to fail. For example,

the term "tall" everyone would agree is fuzzy in the sense earlier

described. But no witness would testify that her attacker was "tall

and not tall"

without inviting the derision of the court, and the fuzziness of the

term will not come to her rescue. I conclude that LC holds in natural

language even for fuzzy terms. Clearly, Earl has a different take on

the matter, but I have been pointing out this simple thought

experiment for a long time now, and I have encountered not a word in

response from anyone suggesting I am wrong. Fuzziness does not failure

of LEM or LC entail.

Moreover, I and other researchers have shown how, within a fuzzy set

theory, purely as a matter of uninterpreted mathematics, LEM and LC

may be upheld.

*> Does fuzzy logic have to be *very* carefully tailored
*

*> to a particular problem?
*

This is not a point of principle. All models are "wrong" by their

very nature. Some, however, are useful. So the goodness of a

model is never an absolute, there are always other considerations

that enter, economy for one. So I would not attack "fuzzy logic"

from this angle. Instead, like Wittgenstein, I seek the "logical

clarification of thoughts", and I apply the same attitude to

Bayes, for example, and to classical stats, both of which can be

useful, even when philosophical foundations are far from settled.

Regards,

S. F. Thomas

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**Next message:**Stephan Lehmke: "Re: Thomas' Fuzziness and Probability"**Previous message:**Tomas Nordlander: "Help! Fussy logic + Expert system = True?"**Maybe in reply to:**Joe Pfeiffer: "Thomas' Fuzziness and Probability"**Next in thread:**Stephan Lehmke: "Re: Thomas' Fuzziness and Probability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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