Regarding possible interpretation of fuzzy propositions. At least
with regards to vague concepts, such as Tall, what we have is
uncertainty, not about the state of the "objective" world, but rather
uncertainty with regards to the semantics of the term. We simply do
not know precisely what Tall means.
If you believe that uncertainty should (at least ideally) be captured
via a probability distribution, this justify a view of fuzzy
membership as a probability distribution over possible interpretations
of this term (perhaps what Pearl had in mind). In the case of Tall,
different interpretations correspond to different intervals. If
accepts the subjective approach to probability theory, then the
decision-maker/analyst should determine what is his/her subjective
interpretation and define a probability distribution.
Since our interpretations of various concepts are not generally
independent, but could have arbitrary relations, Bayes nets could be
useful for describing this relationship, and the truth-functional
operations of fuzzy logic will not, in general apply (as suggested by
Kathy). I have never had the energy to really see how this compares
with the practice and theory of fuzzy logic.
With regards to introducing utility here, that's interesting, but
I would be cautious, as this might complicate the picture
once we want to make decisions (in a clean and justified manner).
Plus, we need a good semantic reason to do so.
Ronen
------- End of Forwarded Message
This archive was generated by hypermail 2b29 : Tue Feb 29 2000 - 05:53:31 PST