From: mailbox@dmitry-kazakov.de   
      
   On Fri, 07 Aug 2009 15:07:26 -0600, Joe Pfeiffer wrote:   
      
   > Bill Silvert  writes:   
   >   
   >> I have been working with decision support tools based on fuzzy logic   
   >> for many years, but recently I have been told by several   
   >> mathematicians that the rules I am using have nothing to do with fuzzy   
   >> logic. I am baffled by this and hope that someone can tell me whether   
   >> there has been a drastic divergence in the definition of fuzzy   
   >> concepts and what these people are thinking of.   
   >>   
   >> The kinds of rules I am using are like those in standard demos, such   
   >> as for buying a house:   
   >> IF the house is close to work AND not too expensive THEN ...   
   >> where one can obtain crisp rules by defining "close to work" and "too   
   >> expensive" in terms of precise distances and prices, but in practical   
   >> terms these are fuzzy concepts and thus a house that is a little too   
   >> far from work might be acceptable if the price is very low (the actual   
   >> rules under debate deal with issues such as nutrient levels). What is   
   >> the basis for saying that this kind of rule has nothing to do with   
   >> fuzzy logic?   
   >   
   > Your description doesn't quite give me a clear idea of how your rules   
   > work -- when you say you can obtain crisp rules by defining "close to   
   > work" it sounds like you're using a boolean value.  But then your   
   > description of "too far OK if cheap enough" it goes back to sounding   
   > fuzzy.   
      
   > So...  if your idea of "close to work" has a value of 0 at 1.5 miles   
   > away or farther, and a value of 1 at .5 miles away or closer, and is   
   > something in between (for instance, a linear function) in between the   
   > two distances, you've got a fuzzy rule and I've got no idea what the   
   > mathemeticians are talking about.   
   >   
   > If your idea of "close to work" is 0 at distances beyond one mile, and 1   
   > for distances at or within one mile, it's crisp.   
      
   There could be another source of uncertainty. The function "close to work"   
   may be crisp but if the argument "distance" is not, the "value" of the   
   function will be a distribution of truth values over distances.   
      
   ---   
   I cannot tell for mathematicians mentioned by OP, but to me any fuzzy   
   concept shall include an interpretation of rules/operations etc. In   
   particular the meaning of truth values, which tells why the numeric result   
   is like it is. The problem with ad-hoc rules used by some people is that   
   they do not care about giving any interpretation that would justify the   
   result obtained.   
      
   To give an example, let us consider the theory of probability. The meaning   
   of "truth value" there is the probability, a set measure. All statistical   
   rules can be tacked down to the probabilities. This justifies the numeric   
   results and gives the premises of use.   
      
   Similarly if we take fuzzy set theory, the only way I see as a   
   mathematician, is to postulate some set measure and consistently apply it   
   in order to get rules of inference, composition etc. The   
   possibility/necessity is kind of such measure.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
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