From: earlcox@earlcoxreports.com   
      
   "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. It is   
   simply their underlying representations that involve sets that allow partial   
   memberships. The result from the pricing model was certainly not fuzzy! The   
   client paid over $239K (about 140K GPB) for the model and used to it make   
   critical line of business decisions.   
      
   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.   
   Again, you speak about the world being stochastic rather than fuzzy -   
   failing to see that there is nothing inherently wrong in accepting that the   
   world can be both. If I say: There is a 50% chance of a light rain   
   tomorrow - I have easily and simply combined randomness with fuzziness. The   
   world is filled with random events. But the world is also filled with   
   fuzziness - concepts of tall, fast, little, big, near, far, close to, etc   
   etc.   
      
   And again, you speak about the firm foundation of fuzzy logic as though   
   fuzzy logic is some kind of heuristic or ad-hoc approach to modeling (like   
   the old certainty factors in MYCIN). Fuzzy logic has a mathematically solid   
   foundation.   
      
   Anyway, I've already spent far too much time on this thread.   
      
   I'm going back to work. I'll let someone else pick up this thread.   
      
   Earl   
      
      
   > > It is more   
   > > reasonable to say that fuzzy logic provides a different epistemology of   
   > > knowledge than Boolean logic and for models that can benefit from this   
   > > epistemological perspective, fuzzy logic can add robustness,   
   > > extensibility, simplicity, and computational power.   
   >   
   > Fuzzy logic is an extension of the Boolean logic. As such it cannot   
   > contradict to what it extends. So it is difficult to talk about different   
   > perspective. However it is indeed a different pespective as compared to   
   > stochastic approach. [Features you refer are (2), i.e. cases when solution   
   > cannot be found, but known to exist.]   
   >   
   > Probably you meant inherently fuzzy cases, where the problem is formulated   
   > in fuzzy terms from the very start. The example you gave could be   
   > interpreted in this way. Well, it is a philosophical question where such   
   > problems could appear in the "real world", in the sense that there is no   
   > and cannot be non-fuzzy model. Many would argue that the world is rather   
   > stochastic than fuzzy. However, I tend to think that some "real" things   
   > could be really fuzzy, especially when human being gets involved.   
   >   
   > > Well, that's all I have on this subject.   
   > > Until non-academics and business consultants start building real fuzzy   
   > > models   
   > > that deal with real, complex, difficult, and nonlinear problems   
   > > and do this for customers who are paying real dollars for the answers   
   > > and start bringing their experience to this news group, then   
   > > all these discussions about the utility of fuzzy logic, when to use   
   > > fuzzy logic, how to use fuzzy logic, etc. is just so much   
   > > poorly thought out and ill-informed speculation.   
   >   
   > We need firm foundations of what we call fuzzy. Otherwise, all successful   
   > examples of its application are no more than naive: "it worked to me". We   
   > need to understand what did work, when it will, and when it won't.   
   >   
   > > "Dmitry A. Kazakov"  wrote in message   
   > > news:c5te15$58ae3$2@ID-77047.news.uni-berlin.de...   
      
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