fb8373f9   
   From: mailbox@dmitry-kazakov.de   
      
   On Mon, 11 Aug 2008 21:32:08 -0700 (PDT), feilian wrote:   
      
   > I have begin some study in Fuzzy regressions. I am not sure about the   
   > meaning of fuzzy numbers.   
   >   
   > I know that for a fuzzy set A, the member function A(x) means the   
   > possibility x belongs to set A.   
      
   Fuzzy real number is a fuzzy subset of R.   
      
   > For a LR fuzzy triangle fuzzy number A=(a,s), what does this fuzzy   
   > number mean? Does it means a interval[a-s,a+s]? And what does it's   
   > member function u(x)=|x-a|/s mean?   
      
   It is the interpretation of a fuzzy set, If A is a fuzzy number A:R->[0,1],   
   then A(x) tells how much x belongs to A.   
      
   > Does it means the possibility x belonging to interval [a-s,a+s]?   
      
   These are two questions:   
      
   1. Yes, if the meaning of truth values is possibility, then, well, it is   
   possibility.   
      
   2. No. A triangular-shaped membership function is not rectangular   
   (interval).   
      
   The possibility of x being in an interval I is 1 if x in the interval, 0   
   otherwise. (You probably meant something else.)   
      
   A final note, the set of fuzzy numbers with rectangular membership   
   functions reaching 1 is fully equivalent to the classical interval   
   arithmetic. Fuzzy numbers of any shape can be considered a continuation of   
   that.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
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