I truly fail to follow your opening statement. Who in the world said that fuzzy logic breaks down? Even on elementary problems? Perhaps I contributed to the confusion by speaking about "rare occurrence" as if it implied that "fuzzy logic fails at these points but it's only rare". I meant to say that the point where B=A and B=~A exactly occurs at this one truth membership point. At all others we have a different, but equally valid, truth membership function. I also fail to see how your example about the eye color addresses anything about fuzzy logic. And why do you suppose (erroneously) that fuzzy logic -- fuzzy set theory in particular -- ignores relationships between compound propositions?? How can anyone in this news group hold reasoned discussions about fuzzy logic if the participants fail to even do basic background reading and research in the principles and mechanisms of fuzzy set theory, fuzzy logic, and fuzzy systems? It seems evident to me that much of the debate incorporates the individual's conjectures about what is and what is not fuzzy logic. 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) "Robert Dodier" <robertd@athenesoft.com> wrote in message news:23af61c2.0108122107.6f0e7aab@posting.google.com...> In reply to the follow statement by Herman Rubin, > >>> 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. > > "Earl Cox" <earldcox1@home.com> wrote: > >> 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. [...] But you are right, a fuzzy system is truth-value based. >> There is absolutely nothing wrong with this. > > If fuzzy logic breaks down on elementary examples, what will happen > in complex problems? > > Consider the mayor of Ashtabula. Let A = "mayor's right eye is blue". > Let B = "mayor's left eye is blue". Let B' = "mayor's left eye is brown". > What do you suppose is the truth value of A B ? What about A B' ? > > The difficulty is that rules of the kind applied in fuzzy logic > ignore relations between the elements of a compound proposition. > > Incidentally, some people do have eyes of different colors. > For all I know the mayor of Ashtabula is one of them. > > Regards, > Robert Dodier > -- > "Nature exists once only" -- Ernst Mach