From: earlcox@earlcoxreports.com   
      
   Bravo Bill!!!!   
      
      
   "William Siler"  wrote in message   
   news:49b9df3d.0401112121.3e799209@posting.google.com...   
   > "Dmitry A. Kazakov"  wrote in message   
   news:...   
   > > EarlCox wrote:   
   > >   
   > > >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".   
   >   
   > It seems to me that Dmitry is using an improper definition for   
   > erroneous. Let me distringuish between "contradictory" and   
   > "ambiguous". Suppose our consequent datum is a discrete fuzzy set.   
   > After firing the rules, suppose that more than one member of this   
   > fuzzy set has a non-zero grade of membership. Is this an ambiguity or   
   > a contradiction? Depends on whether the members of the fuzzy set are   
   > mutually exclusive. If they are not, as in {Fast Medium Slow} we have   
   > a desirable ambiguity, but not a contradiction, an no error. It they   
   > are mutually exclusive, as in {Ford Chevrolet BMW} we have a   
   > contradiction, and should do something about it. We have a   
   > contradiction, but not an error.   
   >   
   > Earl states that if we only fire one of several concurrently fireable   
   > rules, we can get an erroneous result. Surely if firing one rule gives   
   > {Slow/0.5 Medium/0 Fast/0), and firing the next rule gives {Slow/0.5   
   > Medium/0.9 Fast/0}, the state of the discrete fuzzy set after firing   
   > the first rule is incorrect. But where is the contradiction? I'm   
   > afraid that I agree with Earl; when firing several rules concurrently,   
   > the result cannot be considered to be a correct representation of the   
   > state of knowledge until all these rules have been fired. After they   
   > have all been fired, we may have a contradiction, as in {Ford/0.8   
   > Chevrolet/0.5 BMW/0.3}, but that is not incorrect; it may be a valid   
   > picture of the state of affairs up to this point.   
   >   
   > > 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   
   >   
   > No, it does not. But it means that if we know A and B and C ..., the   
   > result of firing the rule "if A then price" does not correctly   
   > represent the state of knowledge. In this sense, the result is   
   > erroneous.   
   >   
   > What this does is focus attention on the necessity for having some   
   > theory to deal with getting a correct consequent truth value when   
   > firing a bunch of rules concurrently. The theoreticians have been of   
   > no help to me at all; in the book on automated fuzzy reasoning I'm   
   > just finishing there are two chapters on the theory of how to handle   
   > this problems in different situations; I had to roll my own theory,   
   > since the theoreticians apparently didn't seem to know that their own   
   > possibility theory was incorrect, and relied on fallacious   
   > methodology. Computer science is not of much help here; in its present   
   > state it is Boolean, and doesn't deal with truth values. The   
   > interesting thing is that Earl and I independently arrived at similar   
   > conclusions without help from the theoreticians   
   >   
   > > > 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.   
   >   
   > It seems to be a fundamental tenet of mathematicians that applications   
   > are uninteresting. This is a development of the last hundred or so   
   > years. Archimedes didn't think that way. When Pythagoras went off into   
   > the wild blue yonder his school's most notable achievement was   
   > murdering a disciple who didn't agree. Certainly Newton, LaPlace,   
   > Gauss and many others at that time were extremely interested in   
   > applications, and viewed them as an inspiration for new mathematics.   
   > Think where the calculus came from. I remember giving a talk at a   
   > NAFIPS meeting in the 1908's pleading for help with some mathematical   
   > problems that my applications brought up; I got none. As a new chair   
   > of the Biomathematics Department at a major university, I gave a talk   
   > to the Mathematics Department asking for help on some applications for   
   > which I did't have enough math to handle. Instead of working on those   
   > problems, they decided to work on the Lotka-Volterra equations, even   
   > though they were known not to be able to account for the experiments.   
   > (I found out without their help that we needed a discrete stochastic   
   > formulation of the Volterra equation, which worked just fine.)   
   > Although I'm a biologist, I'm also a professional software engineer   
   > working primarily in AI in medicine, and I'm getting tired of having   
   > to roll my own theory because the mathematicians aren't interested in   
   > applications. How many fuzzy mathematicians pay any attention at all   
   > to this newsgroup?   
   >   
   > William Siler   
      
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