From: mailbox@dmitry-kazakov.de   
      
   On Wed, 30 Jul 2003 13:01:48 GMT, "project2501"   
    wrote:   
      
   >supposing we simply used the membership values as the coordinates in a   
   >high-dimensional space.   
   >   
   >that would seem logical - but i feel that I would have lost some   
   >information. this the the "ordering" of the fuzzy sets.   
   >   
   >so, "low", "medium" and "high" each have memberships for the variable   
   >"length" - but if i simply use the memberships - then this ordering is not   
   >encoded anywhere.   
      
   No, if you choose this model then, you will have the set of   
   coordinates:   
      
   D x M   
      
   here:   
      
   D is the domain set of "length" = { "low"; "medium", "high" }   
      
   M is the set of membership values, for example some set of   
   subintervals of [0,1]:   
      
   { 0..0.1; 0.1..0.2; ... ; 0.9..1 }   
      
   ---   
   Regards,   
   Dmitry Kazakov   
   www.dmitry-kazakov.de   
      
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