From: earlcox@earlcoxreports.com   
      
   After all the pages of discussion, you still just don't get it. You are   
   still confusing fuzzy logic with the mathematical nature of the model's   
   dependent to independent variable space. In a stochastic model the   
   connections are made through samplings of random points (drawn from some   
   distribution). In deterministic models the connection is made through   
   linear or nonlinear functional transformations. Neither of these have   
   anything to say about the underlying data representation which can be crisp   
   or fuzzy. The logic we select reflects the kind of data we are handed.   
   Simply put:   
      
   Fuzzy logic addresses a universe of problems where the variables have   
   imprecise (but possibly not uncertain) boundaries. As such, it should be the   
   logic of first choice for such problems, whether they are deterministic,   
   stochastic, or magical.   
      
   I have said what I have to say. I think this is my very last comment on this   
   thread -- it's like arguing with a blind man who insists your red car is   
   blue.   
      
   earl   
      
      
   "Dmitry A. Kazakov"  wrote in message   
   news:3s0780lqfcn46n2buf5j1qn77o9souqcli@4ax.com...   
   > On 18 Apr 2004 20:19:46 -0700, wsiler@aol.com (William Siler) wrote:   
   >   
   > >"Dmitry A. Kazakov"  wrote in message   
   news:...   
   > >>   
   > >> As I see it, in descending order of quality: deterministic, stochastic,   
   > >> fuzzy. So fuzzy is the last resort approach, there is nothing after it.   
   > >   
   > >Whether a problem is determistic or stochastic is first a property of   
   > >the problem. There are indeed problems that are basically stochastic   
   > >but that can be treated as deterministic due to the law of large   
   > >numbers. Of determistic problems, many cannot be treated analytically;   
   > >e.g. many nonlinear partial differential equations. In teaching   
   > >modeling of biological systems, I sometimes use a 2x2 matrix; nature   
   > >of problem, deterministic or stochastic, and nature of variables,   
   > >discrete or continuous. One can be seriously misled by "solving" a   
   > >problem by an inappropriate method. Warren Weaver once also had a 2x2   
   > >matrix for problems: organized or disorganized and simple or complex.   
   > >One has to let the punishment fit the crime; select a solution method   
   > >that is appropriate for the problem.   
   > >   
   > >Fuzzy is a set of techniques for solving problems, like solving   
   > >differential equations analytically or Monte Carlo. No one method is   
   > >inherently better than any other, but one method may well be better   
   > >than any other for solving a particular problem. My experience differs   
   > >from Earl's in one respect; while we have many continuous input   
   > >variables, our outputs are seldom numeric, being usually expressed in   
   > >words like "left ventricle", "PAP in RV" or "Catatonic Schizophrenia".   
   > >For problems that require solution by reasoning, fuzzy logic is   
   > >terrific.   
   >   
   > Monte Carlo is a very good example. It is the worst possible method,   
   > which is applied when "good" deterministic ones do not work (for   
   > whatever reason). The situation with fuzzy does not differ. Fuzzy   
   > approach is also inherently worse than both others, but again it might   
   > be the only one which works! So the point was actually trivial: if   
   > crisp sets work, never use fuzzy ones.   
   >   
   > --   
   > Regards,   
   > Dmitry Kazakov   
   > www.dmitry-kazakov.de   
      
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