From: mailbox@dmitry-kazakov.de   
      
   On 10 Sep 2003 04:14:22 -0700, mackinson@hotmail.com (Steve) wrote:   
      
   >I have a question regarding fuzzy inference that I have not been able   
   >to find the answer to on the internet, or books etc.   
   >   
   >Simply it is:  Why is it that MIN-MAX and PRODUCT-SUM inference   
   >options are the most commonly used?   
      
   MIN-MAX corresponds to possibilities. PRODUCT-SUM does to   
   probabilities (under some conditions).   
      
   >Why doesn't anyone mention   
   >MIN-SUM?   
      
   >I have been doing some work where we tried applying MIN inference   
   >(implication) with SUM composition (aggregation of output sets).  It   
   >provided a better result using centroid defuzzification, which allows   
   >for the fact that the summed DoBs of the output sets can be greater   
   >than 1.   
   >   
   >No-one ever seems to talk about MIN-SUM and PRODUCT-MAX inference!   I   
   >can see that there may be a problem with MAX-PRODUCT because it would   
   >result in valleys in the output sets.    What might be wrong with   
   >MIN-SUM?   
      
   It would break de Morgan's laws with NOT=1-x. I do not know whether it   
   is possible to define NOT in a consistent way. Anyway, it also breaks   
   AUA=A.   
      
   >I would very much appreciate any ideas you have or pointers to texts/   
   >examples that could help?   
      
   There is a large amount of papers devoted to the issue. A decision   
   depends on which result of the crisp set theory have to be preserved.   
   It is known that the biggest set is preserved by min/max/1-x.   
      
   ---   
   Regards,   
   Dmitry Kazakov   
   www.dmitry-kazakov.de   
      
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