Rob, Very well said. That misunderstanding about the actual nature of fuzzy logic and fuzzy sets is the principal reasons we have these long drawn out and ultimately futile debates about probability and fuzzy logic. Those who believe that fuzzy logic is simply another form of probability misunderstand the kind of knowledge fuzzy logic is modeling. In some sense this is caused by the fact that both fuzzy logic and probability (a) deal with uncertainty and (b) have a measurement scale in the interval [0,1]. In another, and more general sense, it is because news group participants come to the debate with both preconceived notions about what fuzzy logic is all about and a lack of any real experience with fuzzy models. Earl "Wise" <weiz@spam-block.sympac.com.au> wrote in message news:9kijd0$q5t$1@perki.connect.com.au...> So with some think time off line. > > I am happy with the notion of "Calibration propositions" > (described in the original question) as a means for establishing a fuzzy > sets membership and domain scale relationships. > > The Truth Series, along with a number of other systems, described by Cox > in his book- Fuzzy Systems Handbook validate this method for discovering > a fuzzy sets membership & value pairing. > > So is it probabilistic ? .... In method I would have say that it is. > > BUT > > From an intent and outcome stance there are enormous differences. > > Fuzzy is not a variation of a probability math because you need to discard a > basic foundation of classical set theory required of probability to accept > the > legitimacy of Fuzzy Math. > > When Voting about the probability that a height is tall in order to > yield a probability distribution curve the voters are working to producing > a membership value (% population Yes OR No) that a value is tall OR > is not tall.......... not both. > > When Voting if a height is Fuzzy tall the voters accept the notion > that the height is also not tall. The vote goes to the degree of tallness. > The % of population that vote Tall and that give a fuzzy height value its > membership may also vote that the height is not tall. > > The law of non contradiction must be discarded by those accepting > Fuzzy logic as a valid mathematics. > > Fuzzy means that nothing is either OR --- probability needs only either
OR.> > This is not to say that the mathematics of Probability are not useful. > It is a math method accustomed to processing "degree". In that it doesn't > compromise Fuzzy set contradiction has some useful method. > > Rob W > > Wise wrote in message <9kia7r$kc9$1@perki.connect.com.au>... >> The original question that launched this stream >> talked about >> ########## >> defining a membership function of a set by using >> ``calibrational propositions'' -- the idea is that if >> you ask 100 people if John is tall, and 70 of them say ``yes,'' then >> mu(tall) = .7. While this seems to do a good job of capturing common >> word usage, it's not at all clear to me that it captures the fuzzy >> behavior of the ``tall'' set; >> >> it seems probabilistic rather than fuzzy. >> >> ########### >> >> >> 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 ? >> >> Rob W >> >> >>> >> >> > >