In the words of the great Bezdek (who may have lifted it from Zedah): "If you are crawling acroos the desert and find a sealed box labelled wine and the probability that it contains wine is, say, 0.5; when you open it you find either wine or water and the probs collapse to zero or unity. If the fuzzy membership is .5 water and .5 wine, when you open it you are certain to find sangria. " IMHO fuzzy memberships reflect the degree of hybridness of samples and have nothing especially to do with prob. Robert Dodier wrote:> "S. F. Thomas" <sf.thomas@verizon.net> wrote: > >> You raise a good question. As the author in question, may I >> respond as follows: [...] > > "Responded", and then some. Talk about logorrhea. > > I'm too lazy to quote the whole "Ulysses" of fuzzy logic > here, so I'll just chop off a little flame bait. > >> It is a membership function in the obvious Zadehian sense >> of a point function ranging from 0 to 1, though Zadeh may or >> may not approve of the manner in which it is obtained. > > RUN FOR THE HILLS, Zadeh may not approve! Btw I love your > new adjective for "pertaining to the inventor, nay, the very > Father, of fuzzy logic". My greatest ambition is that someday > people will refer to some function or ice cream or lawn mower > as "Dodierian". > >> This analogy leads to the perhaps startling conclusion that the >> (absolute) likelihood function familiar from statistical >> inference theory is in some sense also a membership function! > > --"Yikes! What was that?" --"Don't worry, dear, it's just a familiar > likelihood function." --"OK, but don't sneak up behind me again!" > >> To treat these two kinds of uncertainty in this fashion is not >> to exalt one over the other, rather to recognize that they are >> inextricably linked, as are the two faces of a single coin. > > Wow, that is, like, so heavy, dude. Hey, I've heard that there > are these guys, who are like monks or something, who teach that > the distinction between myself and the universe is an illusion. > That is, like, so completely far out, man. > >> [...] on the other hand the vain Bayesian attempt to treat >> likelihood as though it were probability, and therefore >> subject to a simple integration method of disjunction >> (evaluation of composite hypotheses or set evaluation). > > This is almost incomprehensible, but it is fun to try to puzzle > it out. I get a vague sense of disapproval of the Bayesian > interpretation of probability. "Dear Abby, my sister says that > I should stop subjecting likelihood to simple integration. I tell > her she's full of hot air, but she won't listen. What should I do?" > >> But this requires both hands to clap: the right hand of probability >> with the left hand of likelihood/fuzzy/possibility. > > Hey, those monks are at it again, man! > >> Hope this is helpful. > > Thanks S.F., I was having trouble sleeping, but not anymore. > > Regards, > Robert Dodier