Dear Herman Bruyninckx,
I am loosing it. Whatever I understood slowly disappears.
Probability theory (or Bayesian theory) is algebraically fully consistent.
Yes, that's why I like it. In fuzzy logic you define rules, which can be
defined in almost infinitely many ways. OK. But the definition of rules in
fuzzy logic is that not a part of the modeling? Has that anything to do
with the algebra of fuzzy sets? Given a fuzzy model, will results not be
"consistent" (in some way) with the modeling? Will results not somehow be
verifiable?
In the modeling aspects BN's (or probability theory) does not offer any
consistency either. Just to take an example from my (engineering) world,
where data often is very scarce --- if not unavailable:
Say you are interested in evaluating a new layout of a bridge design (on a
ship). Your concern is to evaluate the (risk) reducing impact on the
probability of grounding and/or collisions that the new bridge design may
have. In the end, of course, it all boils down to the cost of the new
bridge layout should prove its worth on the reduction in e.g. oil spill.
The new bridge might have effect on available time to detect objects, stress
level, ability to interpret the criticality of the situation, aspects of
weather, traffic, etc., etc. Nonetheless, a (causal) model must be defined
and it is a fiction to believe that there exists such thing as total
objectivity. The choice of model is of course not unique, but it could be
verifiable in a comparison to some data.
I know that BN could help me in such a modeling. But how may fuzzy theory
help? Indeed, aspects of "detection", "stress level", and "interpretation"
are fuzzy. In my BN modeling I also need to define some "rules" on how the
captain will react to combinations of input (or states of the world).
My needs are purely pragmatic. I have no clue on t-norms or t-conorms, which
might be of importance for my writing of the page?
Best regards, Peter
Peter Friis Hansen
Associate Professor, Ph.D.
Department of Naval Architecture and Offshore Engineering,
Build. 101E, Technical University of Denmark,
DK-2800 Lyngby, Denmark
Tel: + 45 45 25 13 88
Fax: +45 45 88 43 25
Email: pfh@ish.dtu.dk
Web: http://www.ish.dtu.dk/pfh/
-----Original Message-----
From: Herman Bruyninckx
[SMTP:Herman.Bruyninckx@mech.kuleuven.ac.be]
Sent: Wednesday, February 23, 2000 11:13 PM
To: Hansen, Peter Friis
Cc: uai@CS.ORST.EDU
Subject: Re: [UAI] Fuzzy sets vs. Bayesian Network
On Wed, 23 Feb 2000, Hansen, Peter Friis wrote:
>
> I have been asked to write a one-page summary on fuzzy sets ---
yet another
> area of which I have no knowledge --- and I therefore would be
interested in
> some clarification on what cases fuzzy set theory is capable of
modeling
> better than Bayesian Network models.
>
My 2 cents ....
Bayesian theory is fully consistent: there is only _one_ way to do
your algebra. While fuzzy logic has an infinite amount of possible
computational rules: all hinges around the fact that there are
infinitely many ways to define t-norms or t-conorms, and there is no
``first principle'' that tells you which one to choose. Therefore,
you
can write an infinite number of papers on the same real system and
the
same data :-) (Which is what many people do indeed :-( )
Hence, fuzzy logic is indeed more general; in fact it is too general
to
be still called a scientific paradigm (because of the
above-mentioned
indefiniteness of its calculus).
--
Herman.Bruyninckx@mech.kuleuven.ac.be (Ph.D.) Fax: +32-(0)16-32
29 87
Dept. Mechanical Eng., Div. PMA, Katholieke Universiteit Leuven,
Belgium
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