Bravo! Zedah's early example centered on an electrical switch that was never really "on" or "off" in that switches tend to leak current. so the degree of "on-ness" is of practical concern. My guess the issue might be the same for transistors, etc. A person can be thought to be a mixture of traits from his forebears so could have a fuzzy membership with respect to father,mother,and the milkman. IMHO the use of fuzzy sets in "expert" systems has been a bit of a stretch and the approach seems not to have the promise it had 15 years ago. So Earl I agree that people can bend and twist the concept to make it a part of statistics; but when they do, they have thrown the baby out with the bathwater. Earl Cox wrote:> The tediousness with which the debate over fuzzy logic and probability > continues, especially among those who have never used fuzzy logic in any > real world application, is absolutely amazing. I am still amazed to hear > absurd statements like: "The fuzzicists CLAIM to have an alternative to > probability..." > > Fuzzy logic and probability are related, but fuzzy logic does not replace > probability. THEY MEASURE TWO DIFFERENT THINGS. Probability the expectation > that an event will occur, fuzzy logic the degree to which it occurred. There > is a 50% chance of a light rain tomorrow. If it rains tomorrow, then the > probability is gone, but the ambiguity associated with the degree to which > the rain is light remains. It is this degree of ambiguity or elasticity in a > concept that gives fuzzy models their power. Fuzzy sets are model dependent. > And if I build a project risk assessment model for a pharmaceutical company > (and I've built quite a few), asking management and/or analysts to vote on > the degree of risk in capitalization, new line of business exploration, the > risk associated with project duration or staffing, and so forth in order to > derive the appropriate fuzzy sets for the model then I have incorporated > their knowledge about risk and their risk tolerance into my model. A fuzzy > case-based reasoning model that predicts the risk of a new project does so > based on the risk aversion and project objectives of the enterprise. > > If anyone reads Kosko, Watkins, etc. they will see that fuzzy inferencing is > not an "ad hoc" mechanism but is based on solid mathematical principles. > > Debating the merits of fuzzy logic with those who come to the debate already > convinced that fuzzy logic is wrong and who have not bothered to even read > the literature, is like discussing a color coordinated outfit with a blind > man. Herman Rubin's message, written without any knowledge of fuzzy logic, > is a perfect example. > > Earl > > -- > Earl Cox > VP, Research/Chief Scientist > Panacya, Inc. > 134 National Business Parkway > Annapolis Junction, MD 20701 > (410) 904-8741 > ------------------------------------------- > > AUTHOR: > "The Fuzzy Systems Handbook" (1994) > "Fuzzy Logic for Business and Industry" (1995) > "Beyond Humanity: CyberEvolution and Future Minds" > (1996, with Greg Paul, Paleontologist/Artist) > "The Fuzzy Systems Handbook, 2nd Ed." (1998) > "Fuzzy Tools for Data Mining and Knowledge Discovery" > (due Early Fall, 2001) > > "Herman Rubin" <hrubin@odds.stat.purdue.edu> wrote in message > news:9kbhja$41p4@odds.stat.purdue.edu... >> The fuzzicists CLAIM to have an alternative to probability, >> but it a mistake in logic which has often been repeated. >> >> The implication many make is that probability is a truth >> value in the sense of logic; it is not. A truth value >> system has the property that the truth value of a compound >> proposition is determined from that of the components. >> The truth value system used in probability is that of a >> Boolean algebra, and probability is a functional on it >> which has certain properties, which happen to make if of >> some utility in application. >> >> Now what happens with fuzzy logic? If the fuzzicists >> were to assign values to compound propositions in a >> consistent way, they would end up with probability. >> If the do not, how can someone decide on a course of >> action under uncertainty? >> >> BTW, the behavioristic Bayesian approach does not >> start out with the prior as probability, but merely >> as the measure corresponding to a positive linear >> operator on utility functions, and it is only the >> product of loss and prior which has implications for >> the course of action. >> -- >> This address is for information only. I do not claim that these views >> are those of the Statistics Department or of Purdue University. >> Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 >> hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558