From: news@williams-home.demon.co.uk   
      
   project2501 wrote:   
   > supposing we simply used the membership values as the coordinates in a   
   > high-dimensional space.   
   >   
   > that would seem logical - but i feel that I would have lost some   
   > information. this the the "ordering" of the fuzzy sets.   
   >   
   > so, "low", "medium" and "high" each have memberships for the variable   
   > "length" - but if i simply use the memberships - then this ordering   
   > is not encoded anywhere.   
   >   
   > ideas, comments gratefully received.   
      
   What are you trying to find distances between ... the linguistic terms or   
   the meaning of those linguistic terms represented by fuzzy sets? .   
      
   This distinction is important as operations you perform on fuzzy sets may   
   not behave the same way as you'd expect the same operations on linguistic   
   terms to behave.  I'm a little confused by your reference to points in a   
   high dimensional space ... whatever else they are the linguistic terms are   
   not points in a high dimensional space ... unless you are considering the   
   product spaces of  sets of linguistic terms and you don't seem to .   
      
   It's often helpful to think through these problems in an abstract linguistic   
   fashion before applying a fuzzy model.  So what is the linguistic distance   
   between high and low for example? and how might you model that with fuzzy   
   sets.   My advice is always to think about how the entities you are   
   representing with your fuzzy sets would behave and model that with your   
   fuzzy sets rather than applying some fuzzy model which doesn't neccessarily   
   model your domain.   
      
   Jon   
      
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