From: mailbox@dmitry-kazakov.de   
      
   On 2016-12-20 10:02, Christian Setzkorn wrote:   
      
   > The TSK system is intended to be used for regression. So the output   
   > is  just continuous. Hence, I do not care about 'theological' debates fuzzy   
   > sets vs. probabilities etc.   
      
   It is the meaning of the calculations done. The "theology" of regression   
   is linear approximation in square mean norm. If the norm is different,   
   regression becomes numerology.   
      
   > I was just wondering how nominal variables   
   > are handled in these situations.   
      
   It is a meaningless question before attaching a good deal of "theology".   
   There are various approaches to substitute a continuous system for a   
   discrete one and back. With fuzzy sets it is called [de]fuzzification.   
   But without "theology" any method and any result is as good as any   
   other. Write the outcome 4.12 be done with it...   
      
   > At the moment I gather that you   
   > recommend to use:   
   >   
   > {Red, Blue, Black, White} -> [0,1]   
   >   
   > Meaning that each category can have a value between 0 and 1. I also   
   > think that these values do not have to be normalized (i.e. add up to   
   > one). is this correct?   
      
   Then it is not a fuzzy set, but a probabilistic set. Probability is   
   additive. Though you cannot say that the sum of probabilities is 1,   
   because for that the events (colors in your case) must be independent   
   and cover all of the color body.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
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