From: mailbox@dmitry-kazakov.de   
      
   On 29 Dec 2005 10:40:00 -0800, rona barca wrote:   
      
   > I want please to ask you about papier or links for transformation from   
   > fuzzy-relationship  to possibilty.   
      
   Normally, fuzzy logic's &, V, not (either min, max, 1-x or their   
   intuitionistic extensions) are associative, commutative, distributive and   
   obey de Morgan's theorems.   
      
   The relation "is" is a tricky one. You should define it with care. When   
   defined as fuzzy subset inclusion it becomes composable with &, V, but in   
   most cases you will have only estimations, rather than equations. This is   
   also true for fuzzy logic in general: when logical values are possibilities   
   then:   
      
      pos (A) & pos (B) >= pos (A & B)   
      
   Left & is "and", right & is "intersection", only ">=" here!   
      
   > I read de paper " Inferring a possibility distribution from empirical   
   > data".   
   >   
   > I'm searching  a few good papers about  Fuzzy-relationships in  the   
   > form   
   >   
   > IF x is Ai  and y is Bi oder z is Ci  THEN t is Di   
      
   That's ambiguous! However, assuming ordering brackets:   
      
   IF (x is Ai and y is Bi) or z is Ci  THEN t is Di   
      
   is equivalent to the pair of rules, accumulated using or:   
      
   IF x is Ai and y is Bi THEN t is Di   
   IF z is Ci THEN t is Di   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
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