From: mailbox@dmitry-kazakov.de   
      
   William Siler wrote:   
      
   > Dmitry is talking about possibility; I am talking about necessity. No   
   > wonder we have massive disagreements.   
      
   I do not think that we have disagreements!   
      
   > To the best of my knowledge, all working fuzzy expert system shells   
   > with single truth values are based on necessity. Systems using our   
   > shell FLOPS include pattern recognition on ulktrasound images of a   
   > beating heart; classification of mineral composition of a rock sample   
   > from its X-ray diffraction spectrum; tutorial program to teach novice   
   > drivers how to deal with an engine that won't start; preliminary   
   > psychiatric diagnosis; alarm system for a neonatal intensive care   
   > unit; and alarm systems for heart transplant and cardiac surgery   
   > inensive care units. All these are single-truth-value systems based on   
   > necessity. Possibilities are computed only when attempting to   
   > invalidate a conclusion previously thought to be true, primarily in   
   > resolving contradictions.   
   >   
   > I don't understand the enthrallment with possibility to the exclusion   
   > of necessity that we find in the literature. Klir and Yuan's index has   
   > 20 entries under possibility or possibilistic, but only one under   
   > necessity. In the real world, we want to know what is true, not what   
   > might possibly be true.   
   >   
   > Nevertheless. I have learned one thing from this discussion; the   
   > importance of necessity/possibility dual truth values. That should   
   > take care of some problems that now require skillful programming to   
   > avoid. It will certainly permit distinguishing between false and   
   > unknown, and enable us to remove tha assumption that a proposition is   
   > false until proven otherwise.   
      
   Exactly my point!   
      
   Necessity does not tell that something is true [*]. It tells that the   
   opposite might possibly be untrue. So formally it isn't better or worse   
   than the possiblity. They are complementary.   
      
   > I'm not clear on intuitionistic fuzzy sets. As far as I can tell, they   
   > require both Nec(A) and a truth value for NOT A, but I don't know if   
   > that truth value is a necessity or a possibility. It also seems, from   
   > earlier Dmitry postings, that one has to give up NOT A = 1 - A, which   
   > I'm quite unwilling to do lacking a compelling reason. The few papers   
   > I have read on intuitionistic fuzzy sets have only confused me.   
   > Obviously Dmitry is well acquainted with intuitionistic sets; perhaps   
   > he can give us a basic, comprehensible explanation of them.   
      
   Actually intuitionistic appoarch could be built on truth values of any kind.   
   It only states that having A does not define notA. The rest follows.   
      
   I tend to apply this approach to the possibility theory, choosing the   
   possibility for the "primary" truth values. One could take the necessity   
   with *exactly* the same effect. It is no matter, because in any case it   
   will end up with possibility-necessity pairs as the "secondary" truth   
   values, with both measures present.   
      
   Then returning to the systems based on solely necessity, I believe that they   
   can be described by fixing the possibility component in 1, thus having   
   (1,*) turth values. Which implies that when such a system yields 1, it   
   means to me (1,1)=true. When it tells 0, it means (1,0)=unknown (note, not   
   false, only maybe false). Of course, when the outcomes are a-priory   
   mutually exclusive, then taking this additional premise, provided that   
   there is one 1-answer, I can refine all 0-answers to (0,0)=false. Is that   
   close to your experience?   
      
   ----   
   [*] Even if Nec(X)=1, that alone does not warranty that X is true. It does   
   only if X is not contradictory. So IF X is not [ Pos(X) >= Nec(X) ], THEN   
   Nec(X)=1 implies that X is certain true.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   www.dmitry-kazakov.de   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)