From: mailbox@dmitry-kazakov.de   
      
   EarlCox wrote:   
      
   > 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.   
      
   Aha. This is a very important point we disagree upon. Erroneous =   
   "contradictory" which is not "unknown". More precisely, "unknown" does not   
   imply (include) "contradictory". So my point is that by substituting   
   "unknown" for any "known" value one cannot achive a contradictory result.   
   The result might be not enough certain, but never contradictory. In other   
   words we might get "reject", but never "error".   
      
   > 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.   
      
   If we have 4 rules about price, it formally means that we want to evaluate   
   price under their conditions:   
      
   price | A & B & C & D   
      
   This is what you mean talking about simultaneity. But this does not prevent   
   us from having:   
      
   price | A   
      
   or even   
      
   price | universum (= "unknown")   
      
   Note that there might be an overseen rule (knowledge), which would make   
   price even more precise:   
      
   price | A & B & C & D & E   
      
   When the set of rules is frozen, then OK we can evaluate everything relating   
   to price before going further. But there might be a situation where the   
   rules come and go, as in the case of a hierarchical system Guillaume talked   
   about. In such system the upper levels may supervise and tune the lower   
   levels. Then the design might be - let's evaluate as much and possible and   
   continue. My point is that the result will remain consistent even then.   
   Further it will be consistent even if rules are fired arbitrarily. It is   
   not about qualitative "error vs. not", but about quantitative "more precise   
   vs. less".   
      
   > 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.   
      
   As a professional software architect I would say that it is not their fault,   
   because IMO, it is not their job. The issue (of dealing with dependent data   
   in an asynchronous system) arise in practically every application area of   
   software development. It is a fundamental software design problem. So it   
   should be taught there. This problem is nasty, sometimes extremely, but   
   doable. And yes, one should avoid it, if one can.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   www.dmitry-kazakov.de   
      
   --- SoupGate-Win32 v1.05   
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