From: mailbox@dmitry-kazakov.de   
      
   On Fri, 08 Apr 2005 22:15:11 GMT, @---@ wrote:   
      
   > Hi,   
   >   
   > example of this classic problem:   
   >   
   > Velocity -> Risk   
   >   
   > Velocity is a fuzzy triangular number divided in the three classical   
   > triangular sets (Low Medium High) (0,0,60 - 40,70,100 - 80,140,140)   
   > (measures in km/h)   
   > Risk is expressed in % through other three triangular sets (Low Medium High)   
   > (0,0,40 - 30,50,70 - 60,100,100)   
   >   
   > The rule system is   
   >   
   > 1) IF velocity is low THEN risk is low   
   > 2) IF velocity is medium THEN risk is medium   
   >   
   > If my velocity is 35 km/h both rules are active with a degree of membership.   
   > I can get my risk level through a defuzzification based on centroid or   
   > weighted average.   
   > So, my output risk is a number between the centoids of the two triangles   
   > (low and medium risk).   
   > If my velocity is 30 km/h i active only the first rule with a certain   
   > membership degree. I can defuzzify using the centroid method and my risk   
   > level is the centroid of the reduced area of low risk triangle.   
   >   
   > But if my velocity is 29 to 0? My output risk level is yet the centroid of   
   > the reduced area of low risk triangle? Is it true or i'ma beginner?   
   > Or better, if my velocity is 0 km/h my risk should be 0 too? Of course.   
   >   
   > Is the centroid method correct or not?   
      
   The problem is not the method of defuzzification, but an incompletely   
   defined sets of linguistic variables. If you take the universal set of   
   linguistic terms: { Low, Medium,  High } and then accumulate it: Low U   
   Medium U High, then the result won't be the universal set of   
   velocities/risk. In other words the relation Velocity x Risk is not fully   
   defined in your case as you might have detected. As a result the outcome   
   could be either unknown (or even sometimes contradictory).   
      
   Because you seems using a non-intuitionistic fuzzy inherence, you cannot   
   express "unknown"=any risk is possible, but none is necessary (or its   
   shades.) Instead of that you will get some arbitrary numbers.   
      
   But that's aside. In any case there is no reasonable way to defuzzify   
   "unknown". So returning to the beginning, the variables you define and the   
   set of rules should be appropriately constrained so that it would   
   *guaranty* that any outcome can be defuzzified. In general case they do   
   not.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)