XPost: sci.math   
   From: earlcox@earlcoxreports.com   
      
   C'mon Bill, correctness, accuracy and precision are two different concepts,   
   and being correct is often context dependent. If I am standing in Yosemite   
   Valley on the road that goes by El Capitan, I can look up the tiny orange   
   figures crawling over the surface. Where are they,   
      
         about 2300 feet   
      
         very high on the rock face   
      
         near Royal Robbin's traverse   
      
   are all correct answers but they are all different. But correctness often   
   has a context component, If you want to know how long it will take a climber   
   to hit the ground if they fall, then, knowing the acceleration due to   
   gravity (I think that's 9.81m./sec/sec),  the first is not only much more   
   correct but has a greater intrinsic utility. If I happen to know where the   
   traverse is located, then the third answer is pretty much equivalent to the   
   first and will also suffice. But the second is not of much help. If I ask   
   you the time, and it's three minutes until four in the afternoon, a response   
   of "four o'clock", "three fifty seven", "three minutes till four", "fifteen   
   fifty seven", and/or "time for tea" might all be correct.We dealers in fuzzy   
   system models should know this well. When we combine outcome fuzzy sets that   
   are scaled according the intrinsic evidence of the rule premises, they form   
   a composite, often irregularly shaped fuzzy set. When this set is   
   defuzzified it yields a scalar solution. But this defuzzification is subject   
   to small "jittery" motions in the precision (or granularity) of the   
   underlying fuzzy sets so that, if we run a model we get a very good but   
   never the less slightly imperfect answer.But the answer, if the model is   
   well built, is correct in the ordinary use of the word!!!   
      
   Just a thought   
   earl   
      
      
      
      
   "William Siler"  wrote in message   
   news:49b9df3d.0409011735.725099bb@posting.google.com...   
   > "Dmitry A. Kazakov"  wrote in message   
   news:<167hedbhbqq7m.7o88pa01l0a0.dlg@40tude.net>...   
   > >   
   > > Note that in general there is no simple answer to your answer. Most of   
   the   
   > > implementation discard possible dependencies between X and Y. This leads   
   to   
   > > less accurate [but still correct] results. Compare it with probabilistic   
   > > equivalent: if you know Pr(X=a) and Pr(Y=b) what would be Pr(X+Y=c)? You   
   > > cannot tell if you do not know the joint distribution of X and Y.   
   >   
   > I understand very well your pointing out the importance of the joint   
   > distribution of X and Y; I agree completely, and wish more people were   
   > aware of this.   
   >   
   > However, I am puzzled by your phrase "less accurate but still   
   > correct". I supppose that "correct" means "without mathematical   
   > mistakes". Nevertheless, it is hard to take in that two different   
   > answers to the same problem could both be correct!   
   >   
   > William Siler   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)