From: mailbox@dmitry-kazakov.de   
      
   On Mon, 06 Oct 2003 19:18:26 +0530, scooter    
   wrote:   
      
   >I've read number of articles about FL and the terminology used is very   
   >confusing. (and contradictory)   
      
   No, see below.   
      
   >Is a FLV comprised of a number of fuzzy sets or is a fuzzy set   
   >comprised of a number of FLVs?   
   >   
   >In other words, Taking the former, I would define HEIGHT as a FLV,   
   >which is comprised of the fuzzy sets: SHORT, MEDIUM and TALL. Is this   
   >the correct terminology?   
      
   Yes. A fuzzy lingustic variable is a fuzzy set.   
      
   So SHORT, MEDIUM, TALL are fuzzy sets. They share the same domain set   
   R+ (set of real numbers representing height, say, in cm). In other   
   words they are fuzzy subsets of R+ or else fuzzy sets over R+. So   
   formally written:   
      
   SHORT : R+ -> [0, 1]   
   MEDIUM : R+ -> [0, 1]   
   TALL : R+ -> [0, 1]   
      
   Now HEIGHT is also a fuzzy set, but it has *another* domain. Its   
   domain set is { SHORT, MEDIUM, TALL }. So formally:   
      
   HEIGHT : { SHORT, MEDIUM, TALL } -> [0, 1]   
      
   This is the whole idea behind the liguistic variables. Instead of   
   working with R+, which is a large infinite set, we are dealing with a   
   very small finite set { SHORT, MEDIUM, TALL }. This is a way humans   
   reduce complexity.   
      
   See also:   
   http://www.dmitry-kazakov.de/ada/fuzzy.htm#linguistic%20variable   
      
   > (In some literature I've seen SHORT MEDIUM and TALL called FLVs and   
   >HEIGHT the fuzzy set! It's v confusing)   
      
   ---   
   Regards,   
   Dmitry Kazakov   
   www.dmitry-kazakov.de   
      
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