From: mailbox@dmitry-kazakov.de   
      
   On Sun, 26 Sep 2004 19:58:20 +0200, Nico du Bois wrote:   
      
   > Fourth: summary   
   > 1. the quotient of two triangular fuzzy numbers is not a triangular fuzzy   
   > number   
   > 2. given matrix A and matrix B: A/B = A * B^-1   
   > 3. there seems to be no Identity matrix existing of fuzzy numbers   
      
   Which should not surprise because the same is true for fuzzy numbers. a/a   
   in general is not equal to 1.   
      
   Returning to matrices, B*B^-1 should contain I in the sense that its   
   diagonal elements will include 1 with the level of truth 1, and other   
   elements will contain 0 also with the level 1. (Assuming that B is normal,   
   i.e. the membership function of each element reaches 1)   
      
   I believe that Mustafa already got the idea. Uncertainty of arguments leads   
   to a definite uncertainty of the result. One could even predict how   
   uncertain it will become, measuring uncertainty of elements of B. Important   
   is though, that the certain result(s) is(are) always included. Say, A and B   
   have for each element the membership function reaching 1 in exactly one   
   point. Then A/B will contain A#/B#, where X# is a crisp matrix of elements   
   where the corresponding membership function reaches 1.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
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