Re: Thomas' Fuzziness and Probability

From: S. F. Thomas (sf.thomas@verizon.net)
Date: Wed Aug 01 2001 - 11:47:41 MET DST

• Next message: Joe Pfeiffer: "Re: Thomas' Fuzziness and Probability"

Stephan Lehmke wrote:
>
> In article <1br8uygr4n.fsf@cs.nmsu.edu>, Joe Pfeiffer writes:
> > I'm currently reading the book mentioned above; I'm wondering about
> > something...
> >
> > He attempts to define the membership function of a set by using
> > what he calls ``calibrational propositions'' -- the idea is that if
> > you ask 70 people if John is tall, and 70 of them say ``yes,'' then
> > mu(tall) = .7. While this seems to do a good job of capturing common
> > word usage, it's not at all clear to me that it captures the fuzzy
> > behavior of the ``tall'' set; it seems probabilistic rather than
> > fuzzy.
> >
> > So, what are other people's reactions?
>
> Same for me. I haven't read the book, but this `voting approach' is
> often used as a justification for membership degrees.
>
> My standard counterexample is an orange.
>
> While nobody in their right mind would say that an orange is `red', I
> bet a lot of people would agree it's at least `somewhat red'. So while
> the probability that an orange would be called `red' might be zero,
> I'd give it a non-zero membership degree in the in the fuzzy set of
> red objects.

I don't see how this is a counter-example. This IMO simply confounds
two different terms, namely "red" and "somewhat red", and implies a
usage which is incorrect in my opinion, namely that for something to
be describable as "somewhat red" is to concede that it is perforce
also "red". I don't think that is necessarily true. It is the same
as
saying that if someone is "not tall" that they are perforce "short".
The implication should rather go the other way; the narrower term
implies the broader, not the other way around. It would be like a
witness testifying in courst that the orange she had for breakfast
was
"somewhat red", or a "reddish orange", only to have a too-clever
lawyer
seek to impeach the credibility or mental competence of the witness
by insinuating that she claimed to eat "red" oranges!
Be that as it may, I don't see that there is any difficulty posed
in principle for a polling procedure that takes an exemplar of
*any* shade of "reddish orange" or of "orange red", or indeed of any
shade of color whatsoever, and obtains its corresponding
characteristic
(membership) value in the manner described, for any term of color,
"red", "reddish", "somewhat red", "orange red", or whatever.

> For empirically finding a membership degree, I'd rather have people
> mark the `degree of tallness' on a continuous scale between `tall' and
> `not tall at all' and take the average.

I don't like it, because your subjects still have to be
told what it is you mean by "degree of tallness". Which is a kind of
circular question-begging in my opinion.

>
> @ARTICLE{Zimmermann/Zysno80,
> language = "USenglish",
> author = "H.-J. Zimmermann and P. Zysno",
> title = "Latent connectives in human decision making",
> journal = FSS,
> year = 1980,
> volume = 4,
> pages = "37-51"}
>
> regards
> Stephan
>

Regards,
S. F. Thomas

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