From: kirk@bytecraft.com   
      
   Dmitry A. Kazakov wrote:   
   > 3. Logic is not geometry. Though it is true that the equation x^2 + y^2 =   
   > r^2 implies under certain conditions certain statements about axes of a   
   > circle defined in a certain way. But it would be silly to expect fuzzy   
   > logic to capture that. Same is true for crisp logic too. Neither is   
   > geometry.   
      
   Admittedly I was approaching the problem from our control   
   background, looking at a circle as just another output waveform.   
      
   >> If we can't describe   
   >> its qualities accurately in human linguistic terms, we might not   
   >> be able to encode it in fuzzy logic.   
   >   
   > You do not need to describe a circle accurately. You can do it   
   > inaccurately, that's the whole idea.   
      
   Meant to say "operably" or similar. In the model I was using and   
   failing with, there is only that curve: no information about,   
   say, the forces that bring it into being.   
      
   > look where uncertainty can come from. For instance, when r is not all   
   > known. So you replace a crisp number r with a fuzzy number. That will   
   > immediately give you a fuzzy set of pairs (x,y) in R^2, which can be called   
   > "fuzzy circle."   
   >   
   > Note that this will yet tell nothing about axes and their relations. You   
   > will need to define them first. It could turn a non-trivial problem.   
   > Neither it is in geometry, BTW.   
      
   Thanks for focusing this problem for me. Always useful to be   
   taken to school every once in a while. ;)   
      
   Kirk   
      
   --   
   Kirk Zurell   
   Byte Craft Limited   
   Waterloo, Ontario, Canada   
   http://www.bytecraft.com   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)