I am interested in a certain question concerning fuzzy logic
and probability. I am trying to figure out whether there are
theoretical reasons to prefer one to the other in an application
concerning the computation of degrees of certainty. (I am using
the term `certainty' informally; I don't want to interpret it
according to any particular theory.)
Here is a little background. I am working on a system to do
failure diagnosis for heating, ventilating, and air conditioning
equipment. I have chosen to use the `Bayesian' interpretation
of probability (apparently due to de Finetti) for modeling
uncertainty in the system. However, there are people for whom
I am working (indirectly) who might ask, ``Well, why didn't you
use fuzzy logic?''
I am aware that proponents of this Bayesian probability theory
claim that it is the only consistent generalization of binary
logic (according to Cox's theorems). Where does this leave
fuzzy logic?
It would appear that if the fuzzy logic concept of `degree of
truth' is the same as the Bayesian `degree of belief,' then
either fuzzy logic is the same as probability or else less
powerful (as it would have to be inconsistent). One could salvage
fuzzy logic by interpreting `degree of truth' differently from
`degree of belief,' but does `degree of truth' then remain useful?
In particular, can one bet on a `degree of truth' ??
I've asked this question before, but got no satisfying answers;
I think it's interesting enough to try again. Please, no homey
parables about murky water. :) (As an aside to S.F. Thomas, my
university's library doesn't have your book, and I would rather not
buy it just to answer this one question; surely there is a brief
answer.)
I apologize in advance for any misconceptions and misstatements.
Regards,
Robert Dodier
-- How Does a Person Decide Whom to marry?? "You flip a nickel, and heads means you stay with him and tails means you try the next one." -- Kally, 9