Lluis,
>This "soft evidence" is actually what possibility theory tries to capture
>and handle and I think there is some work done in relating likelihood
>functions and possibility distributions.
That is interesting.
>There is another ontology, pushed by Enrique Ruspini (SRI), for fuzzy
>membership functions which I personally like, it is to interpret
>membership degrees in terms of similarity in the following terms. Using
>your example, the fuzzy membership of Robbie's adult height in the set
>"tall," in a given context, should be taken as proportional to how similar
>(in terms of height) Robbie is (or will be) to some pre-determined
>prototypical "tall" people in the given context.
In probability models, log-likelihood is often proportional to some kind of
squared distance measure of the data from the parameter, so these two ideas
are not that different.
>However, this ontology
>does not give rise to a fully truth-functional framework.
Soft evidence isn't truth functional either.
I suspect it is generally true that an insistence on truth functionality
cannot be maintained without imposing independence assumptions one would
not want to impose. Remember that the certainty factor people attempted to
develop truth functional uncertainty propagation, and that it turned out to
be untenable except under some rather stringent independence assumptions.
I suspect that when all is said and done we will arrive at either a
likelihood or utility based semantics for fuzzy memberships. I suspect
this will lead us to "graphical fuzzy models." I suspect we will then
discover that propagation of fuzzy memberships will *not* be strictly truth
functional except in cases where the graphical model for the problem is
tree structured. (There, I've just laid out a PhD dissertation topic for
some enterprising student!)
I also suspect that the distinction between likelihood and utility
semantics will blur. I am sure many of you are aware that utilities and
probabilities are not completely separable, but are subject to a sort of
"uncertainty principle" on simultaneous measurement.
>I agree that one thing is to provide meaningful ontologies and another is
>to try to fit them with a bunch of combination rules proposed for fuzzy
>sets, some of them clearly not justifiable. This is a harder problem,
>although there is a growing interest in the fuzzy community to constrain
>arbitariness and at the same time to justify reasoning models on ground
>logical bases. This may lead hopefully to a convergent process.
I would be very happy if the "calculus wars" ultimately led to consensus.
Kathy
This archive was generated by hypermail 2b29 : Mon Feb 28 2000 - 12:11:49 PST