From: mailbox@dmitry-kazakov.de   
      
   Bartosz Bien wrote:   
      
   > I'm building the world out of some crisp and fuzzy pieces (of information   
   > ;)), employing a Mamdani FLC for the decision making. Therefore, some of   
   > my rules utilize both a fuzzy granule and a crisp boolean value, e.g.:   
   >   
   > 1. if A is low then C is bad   
   > 2. if A is high and B is false then C is good   
   > 3. if A is high and B is true then C is very good   
   >   
   > In this example, physically having or not having B (boolean) influences   
   > the decision C when A is high. I am thinking of incorporating such cases   
   > in the double-input-single-output FLC, where input B has two singletons   
   > valued 0.0 - false, and 1.0 - true. Is this approach best or am I missing   
   > a point somewhere?   
      
   I see nothing wrong with that. Actually it is how intuitionistic   
   propositions generalize boolean ones by replacing {0,1} (false, true) with   
   [0,1]x[0,1]. So for an intuitionistic B one considers the pair (Pos(B),   
   Pos(notB)), or alternatively (Pos(B), Nec(B)=1-Pos(notB)). In the latter   
   representation:   
      
   true = (1,1)   
   false = (0,0)   
   uncertain = (1,0)   
   contradictory = (0,1)   
      
   The advantage is that you can handle crisp and fuzzy propositions in same   
   way and you can deal with uncertainty, when, for instance, B is reported to   
   be both true and false (=uncertain/unknown).   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   www.dmitry-kazakov.de   
      
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