From: csetzkorn@gmail.com   
      
   On Saturday, 17 December 2016 15:14:27 UTC, Dmitry A. Kazakov  wrote:   
   > On 2016-12-17 11:36, Christian Setzkorn wrote:   
   > > On Friday, 16 December 2016 10:27:20 UTC, Dmitry A. Kazakov  wrote:   
   > >> On 16/12/2016 10:01, Christian Setzkorn wrote:   
   > >>> On Thursday, 15 December 2016 17:57:45 UTC, Dmitry A. Kazakov  wrote:   
   > >>>> On 2016-12-15 18:41, Christian Setzkorn wrote:   
   > >>>>   
   > >>>>> How do you deal with categorical features (e.g. color, gender) in   
   > >>>>> TSK  fuzzy rule systems used for regressions. Are they encoded as dummy   
   > >>>>> variables, similar to linear regression. Standard fuzzy sets could then   
   > >>>>> be defined on a dummy variable's domain [0 ... 1].   
   > >>>>   
   > >>>> 1. Nominal discrete feature with the enumeration domain: {Red, Blue,   
   > >>>> Black, White}.   
   > >>>>   
   > >>>> 2. Fuzzified continuous domain, e.g. 3-D color space with fuzzy subsets   
   > >>>> defined on it, e.g. Red : Color_Space -> [0,1]. What FCL calls "term".   
   > >>>>   
   > >>>> A fuzzy set over the domain X : {Red, Blue, Black, White} -> [0,1]   
   > >>>>   
   > >>> Just to ensure that I fully understand. So for a nominal variable   
   > >>> with  4 levels: X : {Red, Blue, Black, White} an example fuzzy set would   
   be X   
   > >> : {0.1, 0.3, 0.1234, 0.95643}   
   > >>>   
   > >>> Is this correct?   
   > >>   
   > >> Yes.   
   > >>   
   > >> P.S. fuzzy sets must better be normalized when the norm is Possibility,   
   > >> i.e. reach 1 (fully possible) in at least one point. Assuming that the   
   > >> domain covers all colors, any observed color must yield a normalized   
   > >> set. (Depends on the inference framework, of course)   
   > >>   
   > > Can you please add some relevant links to this so that I can read up on   
   it? Thanks.   
   >    
   > On Possibility theory? It is Dubois and Prade.   
   >    
   > On inference there is a lot of publications, but it really depends on    
   > the system you are going to use, and the type of sets involved. Bare    
   > fuzzy sets, intuitionistic sets, fuzzy-2 sets etc.    
   >    
   > --    
   > Regards,   
   > Dmitry A. Kazakov   
   > http://www.dmitry-kazakov.de   
      
   Hi,   
      
   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. I was just wondering how nominal variables are handled in   
   these situations. 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?   
      
   Thanks.   
      
   Christian   
      
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