From: mailbox@dmitry-kazakov.de   
      
   On 6 Jun 2006 05:50:39 -0700, Hadi Asghari wrote:   
      
   > Dmitry A. Kazakov wrote:   
   >> In my view, the activation function, and/or operators and defuzzification   
   >> are determined by the problem space. When you take PROD and SUM you   
   >> silently assume that the truth values behave as probabilities of   
   independent events.   
   >   
   > Where can I find more information on this?   
      
   If you ask about probabilities and additive measure, then any book on   
   mathematical statistics would fit. If you mean applicability of, then there   
   are quite clear requirements. For example, you need the sigma algebra,   
   random variables etc. The reason why PROD and SUM aren't working is that   
   probably these requirements are not satisfied. If they worked, I would   
   suggested to abandon fuzzy and do it statistically. Maybe you can describe   
   it statistically, maybe not. Same is true for fuzzy based on min/max/1-x,   
   though fuzzy require less premises to be satisfied. Min/max is justified by   
   the possibility theory (see Dubois & Prade books).   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
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