From: mailbox@dmitry-kazakov.de   
      
   On Mon, 12 Nov 2007 00:34:29 -0800, wythe.cheung@gmail.com wrote:   
      
   > I am a new comer for fuzzy. I would like to know what membership   
   > function could I used to create some "roughly circular" (i.e.,   
   > randomly generate some circles and elipse with different sizes).   
      
   (fuzzy /= random)   
      
   The answer depends on the universal set upon which the fuzzy one lives.   
   What is the set where circles are defined? (This is independent on whether   
   we consider random or fuzzy model of uncertainty.)   
      
   Let us take as an example Cartesian coordinate system, i.e. RxR. Then   
   circle were a subset of RxR defined by a second-order equation.   
      
   A rough circle there would be a fuzzy subset of RxR containing the points   
   of the circle with some reasonably high truth values and all others with   
   reasonably low values. That would be the most generic model of.   
      
   More specialized ones could be like making some parameters of the equation   
   fuzzy numbers. The solution of would again be a fuzzy set like above, but   
   the shape of its truth values would be more narrowly defined.   
      
   Usually one does not use the equation parameters and RxR. Instead one takes   
   some "features" = calculated properties of a geometrical figure. Such as   
   thickness, perimeter, connectedness etc. These features are usually   
   ill-defined on pixels and thus yield fuzzy numbers. A rough circle could be   
   a figure which features roughly match ones of an ideal circle. In essence   
   this approach, customary used in image processing, replaces 2D space 2**RxR   
   (the set of all possible 2D figures) with so-called features space.   
      
   One last note. Choosing features is of course an art.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
   --- SoupGate-Win32 v1.05   
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