From: mailbox@dmitry-kazakov.de   
      
   Guillaume wrote:   
      
   >> (...) An advantage of the fuzzy   
   >> intuitionistic approach is that "unknown" is as legal as any other value.   
   >> So C in fact has a value = "unknown". As some rules get fired they impose   
   >> constraints on C, thus making it more and more certain.   
   >   
   > The main advantage of such "intermediate" fuzzy variables is to allow   
   > the expression of, as I said before, "somewhat" abstract concepts.   
   > It's roughly the equivalent of multiple hidden layers in neural   
   > networks. With the advantage of fuzzy logic, which is, amongst   
   > other things, a strongly semantics-oriented system. To put it simply,   
   > fuzzy rules "make sense" by themselves, whereas it's extremly   
   > difficult to say what is doing what in a moderately complex   
   > neural network-based system.   
      
   Yes.   
      
   > I'll take an example: let's suppose a vision-oriented fuzzy system   
   > with a certain number of inputs connected to a set of vision "sensors"   
   > (I'm not getting into great details).   
   > Now, you could elaborate several sets of fuzzy rules, with sequential   
   > dependencies, to express more an more abstract vision concepts: for   
   > instance, a preliminary set of rules could transform input pixels   
   > to very basic shapes like straight lines, high contrast edges, etc.   
   > Then additional intermediate rules could transform the basic concepts   
   > to more abstract concepts, like "complex" geometrical shapes, and could   
   > finally lead to character or shape recognition.   
      
   Yes. This is a typical way of dealing with complexity in software   
   development.   
      
   >> I think that if implemented properly it cannot introduce any additional   
   >> instability.   
   >   
   > Possibly, but by manipulating "fuzzy abstract concepts" in the way I   
   > stated above, I think instability is more likely to happen.   
      
   I do not think so. The word "defuzzification" Earl Cox mentioned in passing   
   is very important. If the results are kept fuzzy, everything should be OK,   
   provided that the "abstract concepts" are consistent [numerically stable   
   etc]. But once you defuzzify, get ready. The problem is that at some stage,   
   you have to.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   www.dmitry-kazakov.de   
      
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