Sigh. We are still missing the core epistemological difference between fuzzy logic and probability. Time to move on. earl "Robert Dodier" <robertd@athenesoft.com> wrote in message news:23af61c2.0108051321.184d83ae@posting.google.com...> sfrthomas@yahoo.com (S. F. Thomas) wrote: > >> "Wise" <weiz@spam-block.sympac.com.au> wrote: > >>> [...] So can a "fuzzy expert" panel of 100 vote on a particular elements >>> inclusion in a fuzzy set (ie that a height is tall) and the extent to >>> which they agree (say 70%) on the inclusion of that element in the >>> set be converted to a membership value ? >>> >>> Then IF the answer is yes why then is this not probabilistic ? >> >> Asked and answered, as they say in court. Yes it is probabilistic, but >> it doesn't make the membership function a probability distribution. It >> makes the membership function what I have called a semantic likelihood >> function, a point function that does not integrate to unity as >> required of a probability distribution, but does range on [0,1] as >> required of a membership function. > > If we follow through on this notion of semantic likelihood, we'll > find that the laws of probability already contain the appropriate > rules for combining fuzzy statements. I'm comfortable with that, but it > does make fuzzy logic less of a breakthrough. > >> I don't think people have appreciated the full implications of that >> insight just yet. It certainly is *not* to say that fuzzy is just >> probability after all, anymore than it makes sense to say that >> likelihood *is* probability. (The Bayesians, in effect, do the latter, >> but they are wrong IMO.) [...] > > If we take that first step of making membership a likelihood function, > we're already done. The laws of probability specify how likelihoods > should be combined with each other, so there's no need to go off and > invent a new logic for that purpose. Incidentally, probability also gives > the rules for finishing the job: how to combine likelihoods with > probability distributions to obtain a posterior over any variable of > interest, linguistic or otherwise; the posterior over non-linguistic > variables is what is needed to compute risks and take actions, assuming > that losses are stated in terms of what's actually happening as opposed > to what somebody says is happening. > > BTW Bayesians don't say that likelihood functions are probability > distributions, so I don't know where the strawman argument above > comes from. > > I'm actually quite sympathetic to the notion of linguistic uncertainty, > calibration, making inferences from one vague statement to another, etc. > It's just that I don't see any good reason to invent some adhockeries > to treat the problem; probability works just fine. Take a look at my > treatment of "Where in the world is Elvis Presley?" in Chapter 1 of > my dissertation: http://civil.colorado.edu/~dodier/papers/dodier.ps.gz > > See also the discussion of sensor models, Chapter 6, for some more > models of the "I can't quite get at what I really want to see" flavor. > > Hey, I'm just doing my part to wipe out insomnia. :) > > Regards, > Robert Dodier > -- > "Nature exists once only." -- Ernst Mach