# Re: Fuzzy logic compared to probability

Tom Whalen (dscthw@gsusgi2.Gsu.EDU)
Fri, 1 Mar 1996 20:38:50 +0100

On Tue, 27 Feb 1996, Robert Dodier wrote:

> 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?

IMHO, the Bayesian subjective probability of a proposition E assumes that E
is either absolutely TRUE or else absolutely FALSE as a description of a
particular state or object. To say that the probability of E is P means
that the proposition is one of a class of propositions with a proportion
P that are absolutely true and a proportion 1-p that are absolutlely
false. If new information arrives yielding a poaterior probability p*,
this means that E can now be assigned to a smaller class of propositions
with a proportion p* that are absolutely true and the remainder
absolutely false.

OTOH, to say that the truth value of a proposition F is M means that the
fit between the proposition and our overall knowledge is better than the
fit of any proposition with truth value <M but poorer than the fit of any
proposition with truth value >M. Note that M need not be a scalar
fraction, though this is often a convenient representation.

This concept of fit is broader than Bayuesian subjective probability; it
is possible, though usually not very productive, even to consider
Bayesian probability as a very limited special case of a measure of the
fit between a proposition and a state of knowledge.

> In particular, can one bet on a `degree of truth' ??

It's not exactly the same as a bet, but one can, and often shuould,
allocate resources to respond to hypotheses in proportion to their truth
values.

Tom Whalen dscthw@gsusgi2.gsu.edu voice (404)651-4080 fax (404)651-3498
Professor of Decision Science
The Georgia State University "Never get angry. Never make a threat.
Atlanta, GA 30303-3083 USA Reason with people." -- The Godfather