From: gchien@n.o.S.p.a.m.protodesign-inc.com   
      
   "William Siler" wrote   
   > tarmat wrote   
   > > Let's say my rules make use of the linguistic vaiable TEMPERATURE as a   
   > > consequent, and one of its member sets, say COLD, fires several times   
   > > during the processing of those rules. Say with the values 0.3, 0.5 and   
   > > 0.9, do I use the maximum, the sum or the average as the value to   
   > > defuzzyfy?   
   > >   
   > In most cases, the maximum (standard OR) is the value to use. You   
   > can't use the sum; in your example this would give a grade of   
   > membership of 1.7! The Combs method uses the average successfully, but   
   > unfortunately this method is not well knwon, and is controversial.   
      
   The other alternative is to use probability-OR, i.e.,   
   (p-OR A B) = A + B - (A x B)   
      
   You can do all three in one ternary operations:   
   (p-OR A B C) = A + B + C - (A x B) - (B x C) - (C x A) + (A x B x C)   
      
   Two things observed:   
   1. The result will not go above 1.0 if the input values are within 0 and 1   
   inclusive.   
   2. With your three input values, you can perform binary p-OR for any two   
   and then another p-OR for the result and the remaining one.  In other   
   words,   
   (p-OR A B C) = (p-OR (p-OR A B) C) = (p-OR A (p-OR B C)) ...   
   which is a good thing for implementing cumulative results.   
      
   [Exercise] Use 0.3, 0.5, and 0.9 as input and convince yourself :-)   
      
   Choosing fuzzy-OR (maximum A B C) or probability-OR will depend upon the   
   nature of your variable in its context.   
      
   --   
   Best Regards,   
   Greg Chien   
   e-mail: remove n.o.S.p.a.m.   
   http://protodesign-inc.com   
      
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