From: tarmat@btopenworld.com   
      
   Thanks for your answers, but please elaborate on the following   
   statement (I'm not mathematically minded)   
      
   --snip --   
   There is an implicit assumption underlying these   
   choices: min/max assumes that the operands aare maximally positively   
   associated; product/sum assumes that the operands are independent; and   
   bounded sum/difference assumes that the operands are maximally   
   negatively associated   
   --snip--   
      
      
      
      
   On 4 Jan 2004 18:23:22 -0800, wsiler@aol.com (William Siler) wrote:   
      
   >"Greg Chien"  wrote in message   
   news:...   
   >> "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 known, 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)   
   >> ....   
   >> Choosing fuzzy-OR (maximum A B C) or probability-OR will depend upon the   
   >> nature of your variable in its context.   
   >   
   >Very true. Actually, there is a wide range of choice among related   
   >operators, ranging from min/max through product/sum through bounded   
   >sum/difference. There is an implicit assumption underlying these   
   >choices: min/max assumes that the operands aare maximally positively   
   >associated; product/sum assumes that the operands are independent; and   
   >bounded sum/difference assumes that the operands are maximally   
   >negatively associated. In the case at hand, all the antecedents point   
   >to the same consequent; it is reasonable to assume that they are   
   >therefore positively associated, and min/max is the way to go.   
   >   
   >William Siler   
      
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