From: mailbox@dmitry-kazakov.de   
      
   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   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)