From: voisin.bruno@'nojunk'gmail.com   
      
   Thank you Dmitry   
      
   I understand what you are saying.   
   Let me please rephrase my question the following way:   
   Do FL practitioners generally use some kind of rule base validation   
   technique?   
      
   Thanks   
   bv   
      
      
   "Dmitry A. Kazakov"  a écrit dans le message de   
   news: 1ed9tf37c9kz0.1gcm5ivmi68fo.dlg@40tude.net...   
   > On Tue, 11 Dec 2007 16:36:10 +0100, bv wrote:   
   >   
   >> Like in the tutorial and many other books, one assumes the rule set to be   
   >> complete. For instance, if one uses 2 variables each being attached to a   
   >> Fuzzy Set made of 3 Fuzzy States, on expects to have 9 rules like   
   >> IF V1_FSi is XXX AND V2_FSj is YYY THEN ...   
   >>   
   >> I have always wondered what consideration must be made when using an   
   >> incomplete rule set (e.g. 7 "AND" rules), and/or a rule sets using other   
   >> operators i.e. using OR, NOT ?   
   >   
   > These are two separate issues.   
   >   
   > 1. If you use an incomplete set, [i.e. formally, there exist points in the   
   > input space (Cartesian product of variable's domains) for which no rule   
   > from the set reaches the truth level 1], then under standard inference   
   > rules you might get a non-normal distribution in the output space (the   
   > outcomes). That is - no outcome reaches the truth level 1. This is not   
   > uncommon, using triangular linguistic variables has the same [undesired]   
   > effect.   
   >   
   > When truth levels are possibilities then, this is a contradiction. [A   
   > distribution of possibilities always reaches 1 somewhere = you'll have a   
   > problem in interpreting what you get.]   
   >   
   > Same is true if variables are intuitionistic. An incomplete set may yield   
   > a   
   > contradictory outcome. For example: possibility could exceed necessity.   
   >   
   > Otherwise it depends on the empiric norm you use.   
   >   
   > 2. There is nothing special in OR. NOT, XOR etc under standard inference.   
   > Assume:   
   >   
   >   not X in A <=> X in ~A   
   >   
   > and apply de Morgan's laws to normalize the rules to the conjunctive   
   > normal   
   > form. Here ~A is the complement set of A. Of course, standard rules honor   
   > de Morgan's laws. But again, if it is non-standard, then the meaning   
   > depends on the norm.   
   >   
   > --   
   > Regards,   
   > Dmitry A. Kazakov   
   > http://www.dmitry-kazakov.de   
      
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