For weeks, I have a long and interesting discussion with Eric Dedieu
<Eric.Dedieu@imag.fr> about this topic, , and, more generally about fuzzy
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
-----------------------------------------------------------
Maurice CLERC
Home Page: http://www.calvacom.fr/calvaweb/Maurice_Clerc/Maurice_Clerc.html
"Le but de la societe est le bonheur commun".
------------------------------------------------------------