Otto Cordero wrote:
>
> Hello
>
> I would like to be more specific about my previous question....
> Lets supose someone is asked to give his estimation about the probability of
> some event, answers like "0.78 of probability" are very unlikely. I would
> expect something as "high probability" or "low probability", here we
> linguistic terms, wich could be associated with fuzzy sets.
> I am asking for more information on how fuzzy sets theory joins with
> probabilty theory to manage this kind of situations.
If I may be so bold, I would suggest you take a look at my _Fuzziness
and Probability_ (1995), available from Amazon.Com. Here is an
unsolicited testimonial ca. 1996 from someone I've never met:
+
JG.Campbell (jg.campbell@ulst.ac.uk) wrote:

<snip>

: I've grappled with "fuzziness vs probability" for quite a few years
: and, in my opinion, S.F. Thomas' book is the closest yet to a
: selfcontained and reasoned, logical discourse on the matter. Yes, it
<snip>

What a lovely ego boost! I do appreciate the very kind remarks...

: Regards,
: Jon Campbell

Best,
S. F. Thomas
+
The original book announcement for Fuzziness and Probability can still
be found on the web at
http://www.science.at/marchives/fuzzymail95/1264.html .
I remember asking much the same question as Otto is now asking back in
1977 when I commenced my Ph.D. program. I was taking a course in
Bayesian probability and statistics at the same time that I was taking a
course in fuzzy set theory. The question that occurred to me was, if we
tossed a thumb tack, and we judged that there was a "high" prior
probability that the tack would fall head down rather than on its side,
how would one use a Bayeslike procedure to reduce the (fuzzy)
uncertainty in that initial probability estimate, based on repeated
actual observations of the outcome on repeated tossings. The result was
my 1979 University of Toronto dissertation entitled "A Theory of
Semantics and Possible Inference, with Application to Decision
Analysis". Many years later, in 1995 as indicated, I finally got it
published in book form. As my career took me out of the Academy, I have
been unable to follow developments as closely as I would like. Still, it
does not escape me that every new generation of students of fuzzy theory
continue to ask the same question that occurred to me so very long ago,
suggesting that the mainstream theory has not yet fully or adequately
addressed the question. There are good "sociological" reasons why that
is so, as the early proponents of fuzzy have sought mightily to distance
the fuzzy theory from the probability theory, fearing that if that were
to happen, it would be forever discounted as "nothing new". We are past
that stage now, I believe. Fuzzy is now a successful, mature discipline.
We can go back and clean up the fundamentals, and in the process, the
answer to the kind of question that Otto has raised would become crystal
clear. At any rate, that is what _Fuzziness and Probability_ sets out to
do. In the process, it also cleaned up some errors in the fundamentals
of Bayesian inference, although that was not what I set out to do. At
any rate, I believe it succeeds, and unsolicited testimonials of the
sort quoted above strengthens me in that belief. You may want to check
it out. You may also want to take a look at various discussions in the
fuzzy archives where the sort of issue you have raised has been
discussed again and again. In particular, take a look at
http://www.dbai.tuwien.ac.at/marchives/fuzzymail96/ , also the archives
for 95 and 97, and do a search on "probability". You will see some
interesting discussion on the intersection of fuzzy and probability,
including from my good net friends Ellen Hisdal and W. Siler as well as
myself.
> Thanks a lot.
>
> Otto
Regards,
S. F. Thomas
############################################################################
> This message was posted through the fuzzy mailing list.
> (1) To subscribe to this mailing list, send a message body of
> "SUB FUZZYMAIL myFirstName mySurname" to listproc@dbai.tuwien.ac.at
> (2) To unsubscribe from this mailing list, send a message body of
> "UNSUB FUZZYMAIL" or "UNSUB FUZZYMAIL yoursubscription@email.address.com"
> to listproc@dbai.tuwien.ac.at
> (3) To reach the human who maintains the list, send mail to
> fuzzyowner@dbai.tuwien.ac.at
> (4) WWW access and other information on Fuzzy Sets and Logic see
> http://www.dbai.tuwien.ac.at/ftp/mlowner/fuzzymail.info
> (5) WWW archive: http://www.dbai.tuwien.ac.at/marchives/fuzzymail/index.html
############################################################################
This message was posted through the fuzzy mailing list.
(1) To subscribe to this mailing list, send a message body of
"SUB FUZZYMAIL myFirstName mySurname" to listproc@dbai.tuwien.ac.at
(2) To unsubscribe from this mailing list, send a message body of
"UNSUB FUZZYMAIL" or "UNSUB FUZZYMAIL yoursubscription@email.address.com"
to listproc@dbai.tuwien.ac.at
(3) To reach the human who maintains the list, send mail to
fuzzyowner@dbai.tuwien.ac.at
(4) WWW access and other information on Fuzzy Sets and Logic see
http://www.dbai.tuwien.ac.at/ftp/mlowner/fuzzymail.info
(5) WWW archive: http://www.dbai.tuwien.ac.at/marchives/fuzzymail/index.html
This archive was generated by hypermail 2b30 : Sat Dec 16 2000  09:32:05 MET