From: mailbox@dmitry-kazakov.de   
      
   On Sat, 05 Feb 2005 11:51:38 GMT, Ulf Nordlund wrote:   
      
   > Dmitry A. Kazakov skrev:   
   >> In my view there should be no place for any weights in a truly fuzzy   
   >> inference system. A rule may have either a truth level or   
   >> possibility/necessity describing our belief in this rule in *fuzzy* terms,   
   >> i.e. within the same fuzzy framework. But if it had a weight, that would   
   >> assume existence of some parallel, competing model of uncertainty/belief.   
   >> If this model is better than fuzzy, then use it instead. If it is worse,   
   >> then throw it away!   
   >   
   > Interesting stuff this. One thing I am not sure I understand though: You   
   > imply there is a difference beteen a "possibility/necessity describing   
   > our belief in this rule", and a simple weight.   
      
   Yes, but see below.   
      
   > Now, if that weight is   
   > used for describing our belief in the rule, then exactly what is the   
   > difference?   
      
   The difference is that if we use some measure of truth for the arguments of   
   the rule, then the *same* measure have to be used for the rule itself. For   
   example, if the measure is the probability (in a stochastic system), then   
   we should talk about the probabilities of A, B, C and the probability of   
   the rule "if A and B then C". If the measure is fuzzy truth level [0,1],   
   then it has to be consistently used throughout the system. Should we   
   introduce a "weight" which is not the truth level, then in fact our system   
   is not fuzzy. It does not mean that we are doing something wrong, it only   
   means that we have a combined measure fuzzy x weight. Though of course, it   
   is desirable to attach some "physical" sense to the weight component:   
   distance in some metric space, for example.   
      
   > [Note: I am not familiar with the concept of "possibility /   
   > necessity", (maybe that is the problem..). Also, I am a geologist, not a   
   > mathematician (so an explanation in plain words would be apprechiated)].   
   > I'm trying to figure out where Yager's priorities fits in here.   
      
   In this case I would consider them mapped to some levels of truth. In   
   reality all rules are fired and their outcomes are combined. Because of   
   different levels of truth, the rules of higher confidence would influence   
   the result more that others. So after defuzzification the result could be   
   same as one obtained by the *heuristic* procedure of firing according to   
   the priorities. In other words, I believe that Yager's approach can be   
   validated as truly fuzzy inference. It would be an interesting though   
   difficult work to formally prove this, and also to show under which   
   conditions this heuristics might stop to work. BTW, as a guess, I wouldn't   
   be much surprised to know that it always works, because possibility is a   
   min-max measure.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
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