# Re: Fuzzy logic compared to probability

Maurice Clerc (mcft10@calvanet.calvacom.fr)
Tue, 27 Feb 1996 18:31:32 +0100

On Wed, 21 Feb 1996 Robert Dodier <dodier@colorado.edu> wrote:

>I am interested in a certain question concerning fuzzy logic
>and probability.
>....
>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?

For weeks, I have a long and interesting discussion with Eric Dedieu
representations.
I can here just summarize.
Three main points :
1) one axiom for the Cox's theorem is that you must have either A or non-A.
This is not necessary in some alternatives models (e.g.possibility theory)

2) fuzzy representations can cope with inconsistency.

3) complete ignorance is formalized differently.Say we know nothing about A and
B. In (subjective) probability theory we say usually pr(A)=pr(B)=1/2 (according to
the indifference principle of James Bernouilli). But some models may say only
poss(A) and poss(B) are uniform fuzzy values.

>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?

You could have a look at "The Interpretation of Fuzziness" of Pei Wang
http://www.cogsci.indiana.edu/farg/peiwang/

Hope this helps,
Maurice

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Maurice CLERC