From: kirk@bytecraft.com   
      
   Dmitry A. Kazakov wrote:   
   > On Thu, 10 Apr 2008 09:54:41 -0400, Kirk Zurell wrote:   
   >   
   >> I was looking for a circle-like figure, specified linguistically,   
   >> which I thought satisfied the OP's query:   
   >   
   > I think this probably could be done as well, provided you first defined   
   > crisp circles linguistically.   
      
   Now I see that goal it a little farther away than previously thought.   
      
    > Surely it will limit the set of possible   
   > shapes to some algebra of canonical shapes and their transformations,   
   > described linguistically. Then you would extend that on the fuzzy case.   
      
   > Further, I think it is a mistake to believe that there is single fuzzy   
   > geometry. Just technically, you should stop somewhere. Truth values are   
   > themselves crisp numbers. If you fuzzify them (fuzzy sets-2), then the   
   > second order truth values will be crisp. There is always a firm crisp basis   
   > below any such generalization. For this reason we can generalize certain   
   > parts of geometric properties, but we cannot do them all. Therefore there   
   > always be many fuzzy geometries.   
      
   Understood.   
      
   You and Bill have given me lots to think about and catch up on   
   before I try this again. Many thanks.   
      
   Kirk   
   --   
   Kirk Zurell   
   Byte Craft Limited   
   Waterloo, Ontario, Canada   
   http://www.bytecraft.com   
      
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