XPost: comp.soft-sys.matlab   
   From: mailbox@dmitry-kazakov.de   
      
   On Sat, 16 Apr 2005 12:22:49 +0100, Fuzzy wrote:   
      
   > The examples I've seen in the fuzzy world all relate to categorising one   
   > item of data at a time.   
   > Are there any straightforward "standard" paradigms out there to classify a   
   > data item based on grouped data results?   
   >   
   > For example, say I have this training data set.   
   >   
   > X =1,2,1,3,4,2,4,1 (interval category)   
   > Y= 3,6,3,6,8,3,4,1 (response)   
   >   
   > As we can see from this toy data the highest or "best"  response may be seen   
   > to be around 4 tailing away from this.   
   >   
   > So, when I have a new data item to classify, say a 3, I can give a   
   > prediction for its response. Linguistically, I would wish to classify as a   
   > "Preference", Say "most preferred", "neutral", "least preferred" - I know   
   > how to defuzz, I'm just stating this to give a flavour of what I'm after.   
   >   
   > I know I can use standard distribution stats such as mean and standard   
   > deviation, but I wondered how the fuzzy world would view this problem. In   
   > fact would a method be to formulate the fuzzy sets based on such   
   > distribution stats.   
   >   
   > Any thoughts, references etc appreciated.   
      
   To apply fuzzy you need to formulate the problem in fuzzy terms. The   
   problem of approximation of a function is not automatically fuzzy. Neither   
   it is statistical. It might become statistical first when Y(X) is   
   considered as a random variable with some distribution and the goal is to   
   find the parameters of the distribution which would minimize the   
   probability of an error. This is how we come to mean and dispersion,   
   regression, least squares etc. Alternatively the meaning could be a   
   distance treated as, say, energy of a physical process and again the result   
   might be least squares etc. Nothing changes here with fuzzy. It might   
   become fuzzy if for instance, the values of X and Y are fuzzy, or the   
   function is searched in a class of fuzzy-valued functions etc. Once you   
   have a fuzzy formulation of the problem, "preference" receives a meaning.   
   Then you can expect Y*(3) yielding a fuzzy number. The membership function   
   of this number would represent the expectations of particular numbers to be   
   members of true Y(3). Most preferred would be ones with the highest truth   
   values.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
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