From: rshepard@salmo.appl-ecosys.com   
      
     No matter whose definition of idempotency I read I still cannot grok it   
   and understand its importance to fuzzy logic. The definition in Klir and   
   Wierman [1] is a representative example:   
      
     For all a within [0,1], h(a,a,a,a,...,a) = a, where h is an averaging   
   function of the form (using LaTeX math mode symbolism) h:[0,1]^m --> [0,1].   
      
     I read this as "the average of all a is a".   
      
     Under what circumstances does this arise and why is it an important axiom   
   for characterizing fuzzy set operators?   
      
   Rich   
      
   --   
   Dr. Richard B. Shepard, President   
   Applied Ecosystem Services, Inc. (TM)   
      
      
   [1] Klir, G.J. and M.J. Wierman. 1999. Uncertainty-Based Information:   
   Elements of Generalized Information Theory, Second Edition. Physica-Verlag.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)