From: mailbox@dmitry-kazakov.de   
      
   On 4 Dec 2006 16:22:25 -0800, hmhallani@gmail.com wrote:   
      
   > Someone asked me what was supposed to be an easy question: What does   
   > the y-axis represents in the Membership Function? I know it is the   
   > degree to which an input belongs to the appropriate fuzzy set. But the   
   > person said, i need a more tangible answer.   
   >   
   > So please can you give me an answer to this question.   
      
   It is a conditional set measure mA. The set being measured is the singleton   
   {x}. So y=mA({x}). Any meaning of m is beyond the scope of the fuzzy set   
   theory. In possibility theory m means the possibility that {x} belongs to   
   the set A:   
      
      y=pos(A|{x})   
      
   In probability theory it would the probability of.   
      
   In general it is the theory of uncertainty you take, which assigns a   
   "meaning" to the measure. However, any such theory would do this in some   
   opaque terms like "probability" or "possibility," which themselves cannot   
   be explained and taken for fundamental, intuitively defined. (Actually   
   there were many attempts to reduce probability to something else. None of   
   those was any successful. In my view it were just impossible to do.)   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)