Re: Fuzzy logic compared to probability

Howard Clyma (hclyma@engecs1.unl.edu)
Fri, 1 Mar 1996 21:51:47 +0100


On Tue, 27 Feb 1996, Robert Dodier wrote:
> 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 have seen some references on fuzzy statistics, but I can not find them
right now. I will look at write you later.

A good starting place for discussion of fuzzy logic versus probablility
is IEEE Transactions on Fuzzy Systems, Vol. 2, No. 1, February, 1994.
There is a debate between co-authors Laviolette and Seaman of an invited
letter, and the numerous other authors that replied to their letters.
The editorial by James Bezdeck

Bezdek, J.C. 1994. Fuzziness vs. probability - again (!?).
Editorial. IEEE Trans. on Fuzzy Systems. V. 2 (1). pp. 1-3.

Bezdek, J.C. 1994. The thirsty traveler visits Gamont: a rejoinder
to "Comments on fuzzy sets -- what are they and why?"
IEEE Trans. on Fuzzy Systems. V. 2 (1). pp. 43-45.

I have never gotten a copy of "Fuzzy sets -- what are they and why?"
IEEE Trans. on Fuzzy Systems. V. 1(1) pp. ??

Our library does not have this volume. This discussion and the
references in these papers should be a good starting point.

A less technical discussion but still well done is in Cox's book Fuzzy
Systems Handbook. AP Professional. Academic Press, Inc. Cambridge, MA.
1994.

I hope that this helps.

Sincerely,

Howard
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