From: mailbox@dmitry-kazakov.de   
      
   On 13 Oct 2006 22:52:25 -0700, Sampath wrote:   
      
   > I mean, we can take fuzzy sets ( a mapping from X to [0,1] ) and form a   
   > topology for the set X.   
   >   
   > We can compare the properties of general topology and fuzzy topology.   
   > There is a hope that there are a lot of changes between fuzzy topology   
   > and general topology.   
   >   
   > I need more ideas and information about fuzzy sets and the papers   
   > published in this topic.   
      
   It is not my research area, so for what it is worth... All references to   
   fuzzy topological spaces, I saw, were spaces stratified in accordance to   
   the membership function level. I.e. for each value from [0,1] we'd have a   
   space. One could also consider alpha-cuts as topologies, I think it would   
   be more interesting. That is quite straightforward and gives you fuzzy   
   shapes. What is more intriguing to me would be to fuzzify the distance   
   metric. I.e. to get fuzzy transformations of shapes, crisp or not. Maybe   
   fuzzy shape and fuzzy transformation is eventually the same thing, maybe   
   not. See the disclaimer above.   
      
   Just my two cents...   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
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