From: mailbox@dmitry-kazakov.de   
      
   On Sun, 10 Apr 2005 19:45:44 +0200, Dmitry A. Kazakov wrote:   
      
   > On Sun, 10 Apr 2005 18:08:49 +0200, Guillaume wrote:   
   >   
   >> Nico du Bois wrote:   
   >>> In short, the problem is that your sets are not well defined. There must be   
   >>> a symmetrical overlap at 50% membership for triangular sets. And that is   
   >>   
   >> This is a very strong statement.   
   >> I beg to differ. There *has* to be some overlap, but it *doesn't have*   
   >> to be necessarily 50%.   
   >   
   > Actually it is even stronger than that. It need to be 100%, otherwise   
   > accumulation might be not an upper estimation of the true set. I.e. in the   
   > example given. Let R be the true risk and R* be risk evaluated as an   
   > accumulated result of some set of inference rules, then R(r)<=R*(r)   
   > requires the intersection of all terms to be the universal set. This is a   
                       ^^^^^^^  union, I mean   
      
   > fuzzy analog to Bayesian full group of events.   
      
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
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