From: mailbox@dmitry-kazakov.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.   
      
   > 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...   
   >> Will Dwinnell wrote:   
   >>   
   >> > Luko wrote:   
   >> > "where and why not use fuzzy?"   
   >> >   
   >> > "Dmitry A. Kazakov"  wrote:   
   >> > "If you know for sure that your case is deterministic or stochastic,   
   >> > then do not use fuzzy."   
   >> >   
   >> > Could you clarify what you mean by this?  By "case", do you mean the   
   >> > problem or the solution?   
   >>   
   >> I intentionally used the word "case", because even if the problem itself   
   > is   
   >> formulated in a deterministic or stochastic way, there could be place for   
   >> fuzzy approach. One should also count in our knowledge about the problem   
   >> and the solution space.   
   >>   
   >> 1. The problem can be ill defined. We might know that a system is, say,   
   >> stochastic, but we could be unable to describe in a representative,   
   >> correct, unambiguous way.   
   >>   
   >> 2. This knowledge can be inexact to find a solution in original terms of   
   > the   
   >> problem.   
   >>   
   >> 3. The solution can be inappropriate for some reason (numerical   
   > complexity,   
   >> instability etc).   
   >>   
   >> > And what other choices do you imagine than   
   >> > "deterministic or stochastic"?   
   >>   
   >> As I see it, in descending order of quality: deterministic, stochastic,   
   >> fuzzy. So fuzzy is the last resort approach, there is nothing after it.   
   >>   
   >> --   
   >> Regards,   
   >> Dmitry A. Kazakov   
   >> www.dmitry-kazakov.de   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   www.dmitry-kazakov.de   
      
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