From: mailbox@dmitry-kazakov.de   
      
   On Sun, 10 Apr 2005 23:55:27 +0200, Guillaume wrote:   
      
   > Dmitry A. Kazakov wrote:   
   >> Actually it is even stronger than that. It need to be 100%, otherwise   
   >   
   > 100% overlap? Sorry? Care to elaborate on that?   
      
   As I said, for any x there must be a term Ti such that Ti(x)=1. Otherwise   
   the crisp singleton {x} will be classified [=fuzzified] into a *non-normal*   
   fuzzy subset of {Ti}.   
      
   For example: x=35 km/h. Fuzzification of {x} gives: {Low:0.5, Medium:0.5,   
   High:0.0}. This set is not normal.   
      
   P.S. Normality is required for almost all estimation results, especially in   
   conditionals which appears in inference rules like "if A then B". It is   
   based on the conditional B|A. And when A is not normal then   
   Pos(B|A)>=Nec(B|A) might be wrong <=> B|A is contradictory. There is   
   nothing irreparably wrong with contradictions. Intuitionistic inference can   
   handle contradictory data, but when it comes down to defuzzification you   
   might have a great problem: the result is contradictory, but the actuator   
   requires a value which is a-priori known to exist, then it is no more a   
   contradiction in data, it is one in the model. Which model is then wrong.   
   Here you are.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
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