From: earlcox@earlcoxreports.com   
      
   Technically the earth is an oblate spheroid. Naturally, the outcome of a   
   fuzzy rule is the  dependent variable in terms of the dependent-independent   
   variable relationships. That aside, there is a BIG difference between the   
   idea of "unknown" as a testable state of variable and the idea that the   
   value of a fuzzy outcome cannot be known until all the rules are fired.   
   Intermediate values of the under-generation outcome fuzzy set are simply   
   erroneous until then. Consider the simple pricing model that  comes from a   
   real client and I use in several of my books,   
      
   our price must be High   
   our price must be Low   
   our price must be around 2*MfgCosts   
   if the competition_price is not very High   
     then our price should be close to the competition_price   
      
   The value for "price" is dependent on the evaluation of all four rules   
   before it comes into existence. If the model was re-written:   
      
   our price must be High   
   if price is below avg(retail_price)   
      then profitability is good;   
   our price must be Low   
   our price must be around 2*MfgCosts   
   if the competition_price is not very High   
     then our price should be close to the competition_price   
      
   this second rule -- even assuming a reference to a fuzzy outcome variable   
   automatically invokes defuzzification -- would make almost no sense at all.   
   It is not that the variable "price" has a value of Unknown (which I suppose   
   is technically true) but that even given this state, you cannot use "price"   
   in the antecedent of other rules until you have completely established its   
   shape. And given the way that fuzzy rules are executed, you cannot, in any   
   practical way, even check for the value of price as Unknown and then take   
   some other action. Both information and control systems work in this way   
   (see, as an example, my 1992 article in IEEE Spectrum, "Fuzzy   
   Fundamentals"). Perhaps my previous comments on parallelism were a bit   
   misleading (although that's the way I tend of it). It is not so much that   
   fuzzy rules are run in parallel, but that all the fuzzy rules for the same   
   outcome variable are effectively run simultaneously to derive a value.   
      
   But simultaneity in a fuzzy rule base is a meta-control feature of the   
   underling inference engine. All rules for each of the outcome variables are   
   run together in a simultaneous fashion to generate a set of outcome values.   
   These outcome values can then be used in the antecedents of rules that are   
   not part of the simultaneous rule sets. This is the purpose of Bill Siler's   
   Blocks and my Policies -- to separate out the fuzzy rules form the crisp or   
   hybrid rules.   
      
   It is a major failing of our schools that not only don't they teach the true   
   epistemological and methodological properties of fuzzy logic and fuzzy   
   systems, but even when they do address fuzzy logic, they almost never teach   
   HOW to build and implement a real fuzzy system. This is basically because so   
   few academics have any real work exposure to fuzzy models.   
      
   enuf said.   
   Earl   
      
      
      
      
   "Dmitry A. Kazakov"  wrote in message   
   news:btokdc$9g6ab$1@ID-77047.news.uni-berlin.de...   
   > Guillaume wrote:   
   >   
   > >> Not necessarily. You must remember that a fuzzy system is, in effect, a   
   > >> parallel processing system. All the rules are essentially run in   
   parallel   
   > >> as   
   > > (snip)   
   > >>    if A is High and B is Low then C is Elevated;   
   > >>   
   > >>    if C is Elevated then D is Small;   
   > >   
   > > I believe that to be actually a big limitation with "ordinary" fuzzy   
   > > systems. Sequential rules (as in your example) could prove very useful,   
   > > in my opinion. That would allow to build systems with much higher an   
   > > abstraction level. Whether it would not exhibit some nasty stability   
   > > problems is an interesting project to work on.   
   >   
   > Technically C is a dependent (evaluated) value. It is well possible to   
   build   
   > a "non-ordinary" (:-)) fuzzy system which would deal with that. However it   
   > will have a more complex design. The value of C is initially unknown until   
   > some of the rules it depends on get fired. An advantage of the fuzzy   
   > intuitionistic approach is that "unknown" is as legal as any other value.   
   > So C in fact has a value = "unknown". As some rules get fired they impose   
   > constraints on C, thus making it more and more certain.   
   >   
   > I think that if implemented properly it cannot introduce any additional   
   > instability. Well, it is known that data driven parallel systems are very   
   > difficult to predict as opposed to the systems designed using a   
   > conventional procedural approach, but that is another story.   
   >   
   > --   
   > Regards,   
   > Dmitry A. Kazakov   
   > www.dmitry-kazakov.de   
      
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