From: mailbox@dmitry-kazakov.de   
      
   On Mon, 19 Apr 2004 01:35:39 GMT, "EarlCox"   
    wrote:   
      
   >"Dmitry A. Kazakov"  wrote in message   
   >news:c5una7$5ufrs$1@ID-77047.news.uni-berlin.de...> EarlCox wrote:   
   >>   
   >> > I have a difficult time understanding this hierarchy. Why should fuzzy   
   >be   
   >> > a last resort? Fuzzy logic is a system of logic in the same way that   
   >> > Boolean logic is a system of logic. It is essentially (but not   
   >necessarily   
   >> > always) a logic of continuous variables. It is possible to introduce   
   >fuzzy   
   >> > logic as the logic of choice into almost any modeling approach.   
   >>   
   >> Why one should need fuzzy logic, if the conventional logic would give   
   >*same*   
   >> result? An additional complexity is only then necessary when it gives   
   >> something new. This is what I meant. When fuzzy logic starts to work, it   
   >> shows its strength in giving inexact results (similar to statistics). This   
   >> strength is also its weakness, we might get a fuzzy answer where an exact   
   >> one exists. As for stochastic problems, the situation is worse. Fuzzy is   
   >> not an extension of random, though it might be viewed as a very rough   
   >> estimation of it. This is why I consider fuzzy as the last resort to be   
   >> used when other approaches do not work. Fortunately or not, quite often   
   >> they do not.   
   >>   
   >   
   >Fuzzy logic does NOT give inexact results!   
   >   
   >See, this is the problem!!!! This is the result of inexperience and a   
   >confusion of name with mechanism. Fuzzy logic is not a statistical approach   
   >nor does it have behaviors that are like statistical models. Fuzzy models   
   >produce valid, concrete, precise, reliable and definite results.   
      
   Of course not. The sole idea behind fuzzy is to express uncertainty   
   and to deal with it. Uncertain is not precise.   
      
   >The rest of all this commentary is equally confused. Of course Fuzzy Logic   
   >can contradict Boolean Logic. The intersection of A and Not-A is not an   
   >empty set, as a trivial example, since set membership is not dichotomous.   
      
   It is a silly example. This is not a contradiction. True that not   
   every result of Boolean logic holds in fuzzy. But carefully observe,   
   that it will, if all sets involved are crisp. This is what "extension"   
   means mathematically. The important consequence of this is that you   
   cannot get different answers on the same data.   
      
   --   
   Regards,   
   Dmitry Kazakov   
   www.dmitry-kazakov.de   
      
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