malcolm McCallum wrote:
Maybe this will help...
Imagine you have two people sitting at a table drinking and you are
the waiter/waitress.
One customer says, "I have 13.21435343234 ml of alchohol in my drink."
The other says, "My drink is low."
Which is more meaningful??? When the first person makes their
statement, do you really know what it means? You will need a lot more
information to assess what it means such as: how big is their glass,
how much ice is in it, was it a mixed drink?
The second person has relayed a very useful statement that tells you
exactly what is meant, however, you do not know how much it will take
to fill the drink.
The first example would be a standard estimate such as probability.
It seeks to get to the exact number of concern.
The second exaple is a fuzzy estimate, and provides a cognitive
estimate that has obvious meaning but will need further investigation
to work out the details.
Standard estimates deal with what is probable.
Fuzzy estimates deal with what is possible.
does that make sense?
Not really!
The first statement is (overly!) precise, and has no probability
associated with it. What it means depends on context, and
understanding that is outside of formal mathematics, of any sort.
TBH, I think it's a red herring that confuses rather than enlightens.
The second statement is vague. Whether one deals with it as with
probability or fuzzy logic depends on whether you see the vagueness as
ontic or epistemic.
If one thinks that there is a precise concentration of alcohol, and
that "low" is an estimate of this, then the vagueness is epistemic, so
one could set up a probability model for the concentration.
Alternatively, one might view "low" as an objective category, where
there are some concentrations that everybody would say are "low", and
some where everybody would say that they are "high". But there are
also concentrations in between where any person is not sure whether to
say it is "low" or not. In this case, we might view "low" as being a
vague property, and assign a non-integer truth value to the statement
"the concentration is low", e.g. it might be "60% true". Note that
this would be done even if the concentration was known exactly. The
problem is not one of uncertainty about the actual concentration
(which is what Bayesian probabilities measure), but about vagueness in
the mapping of the exact value to the notion of "low".
Bob
--
Bob O'Hara
Department of Mathematics and Statistics
P.O. Box 68 (Gustaf Hällströmin katu 2b)
FIN-00014 University of Helsinki
Finland
Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax: +358-9-191 51400
WWW: http://www.RNI.Helsinki.FI/~boh/
Blog: http://network.nature.com/blogs/user/boboh
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