You picked the middle point of a fuzzy continuum to comment on this truth equivalence. This point is not only a rare occurrence in a real fuzzy system but is simply a special case where the truth values just happen to be equivalent. How about a fuzzy cardiovascular analysis system that has a rule set like, if height is Tall then risk is increased; if height is Short then risk is slightly decreased. The concepts Talll and Short are not bivalent, but represent continuous, overlapping truth membership functions. The result m(height is Tall) AND m(height is Short) is NOT 1/2 AND 1/2 but the truth membership depends both on the actual value of height and the topology of the fuzzy set. In any case the resulting set in not NULL. But you are right, a fuzzy system is truth-value based. There is absolutely nothing wrong with this. Fuzzy logic is NOT probability, it defines (in the vast majority of cases) an entirely different measure of uncertainty. Tell you what I'll do, Herman, I'll send you a copy of my Fuzzy System Handbook (with the new CD). I'll give you a call next week to get your address. best regards 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:9l4lb6$2h4a@odds.stat.purdue.edu...> In article <%yKc7.52091$m8.16672957@news1.rdc1.md.home.com>, > Earl Cox <earldcox1@home.com> wrote: >> I suppose the statements: > >>> The important distinction is not >>> between bivalent logic and multivalent logic, but between >>> meta-language and object language. A bivalent logic in the >>> meta-language is perfectly adequate for the purpose of modeling the >>> fuzziness in the object language. > >> must make sense to someone. But any metalanguage >> that can convert two-valued logic into continuous valued >> logic must be, at heart, fuzzy logic (since this is exactly >> what fuzzy logic, via the extension Principle, does.) > > I repeat, nobody has been able to make anything sensible > in the form of a linear continuous truth-value system. > Probability is not a truth-value system, but a scale > resting on a Boolean one. > > In any truth-value system, the truth of a statement made > by combining other statements with logical operators > depends only on the truth-values and the operators. The > truth-value of A OR B depends ONLY on those of A and B. > If A has truth-value 1/2, and B has truth-value 1/2, the > truth-value of A OR B is the same if B=A or if B = ~A. > > Probability is NOT truth-value, and does not try to be. > Fuzziness tries to be. > -- > 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