From: barabucc@cs.unibo.it   
      
   Il 6 Jun 2004 19:42:43 -0700, William Siler scriveva:   
   >> if x == DARK then y = MORE   
   >> If I understand correctly this leads to an new set that is the alpha-cut of   
   >> the original MORE set with alpha = confidence of the first rule.   
   >   
   > Only if we use the min AND operator. The operator "a AND b = ab" is   
   > also used.   
   the AND operator... now the AND operator appears out of the blue.   
   Are we reducing the => (implication) operation to a sort of inverse of an AND   
   operation? like "a AND b = a", "b = a AND^-1 a"? (please, let me misuse the   
   math notation)   
      
   If so "a" is 'x == DARK' confidence and "b" is 'y = MORE' confidence.   
   When AND is the min operator "b" is restricted to the value "a", when   
   AND is the * operator "b" should be 1/a. But this is inacceptable   
   because b range would be [1;+oo).   
      
   After a lucky research [1] I found that when then AND operator is min, the   
   implication is expressed as (A => B) = max[1-A, B]. Otherwise, when we   
   use the * operator, we have (A => B) = 1 - A + B - [1-A]B. The latter   
   probably comes from the probabilistic field.   
   But how is the formula for implication derived from the choosen   
   operator? I don't think it's plain algebra.   
      
   >> Is OR the only used operation to combine derived membership functions?   
   >> I fear it is too 'aggressive' for my use, but maybe I just need to   
   >> redefine the starting membership functions for output.   
   > In this case, it's appropriate to use the OR operator. I don't know   
   > what you mean by "too aggressive".   
   with max as OR operator, I keep on getting the most "activated" rule,   
   those that have an activation level of .1 don't impact the output value.   
   I think this is my fault, as I should choose better value for output   
   sets.   
      
   >> Just for my interest, what notation are you using?   
   >   
   > Rules like "if x is DARK then y is MORE" have disadvantages for   
   > general use. It combines fuzzification, inference and defuzzification,   
   > three separate operations, into one rule.   
   For my target this is an advantage :). I aggree with you that this way   
   of dealing with fuzzyness is too restrictive, but for the first project   
   of an undergrad in the field of fuzzy logic I wouldn't like to take too   
   much in a single shot.   
   > In short, we have a   
   > real rule-based fuzzy AI language, defined by Backus-Naur Form (BNF).   
   > This gives us a lot of power. Try solving even toy AI problems, like   
   > the Tower of Hanoi, with fuzzy control rules!   
   Are you talking of the FCL language? I found many fuzzy rule based language   
   around the internet, but this seems to be an official one (ANSI backed).   
      
   > Yes, indeed. William Combs has a very exciting inference method he has   
   > called the Union Rule Configuration   
   I read of it in a previous usenet post. Sadly I have no access the to   
   IEEE to get the full text PDF.   
      
   > It takes experience in   
   > actually constructing working systems over a few years to acquire any   
   > real understanding.   
   A (My) long journey starts with a single step.   
      
   Thanks for the answers, the clarification and all the other info you and   
   the other ppl on the ng gave me.   
   I hope this thread will be helpful to other students in search of a simple   
   and practical expaination of rule evaluation.   
      
      
   [1] http://plaza.ufl.edu/badavis/CIS6930_Project1.html   
      
   --   
   Gioele Barabucci    
   ) http://cs.unibo.it/~barabucc   
      
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