From: mailbox@dmitry-kazakov.de   
      
   On 6 Jun 2005 09:57:54 -0700, Silvert wrote:   
      
   > Although Diego is technically correct,   
      
   It depends...   
      
   > I have always felt that this   
   > definition of fuzzy subset is a bit sterile. It implies a more precise   
   > specification of the membership function than is usually meaningful,   
   > and in some cases, where one can normalise the membership function by   
   > specifying the area under it, it makes subsets impossible. I would like   
   > to see a more useful definition with examples of how it can be applied.   
      
   It is a classical definition of the inclusion relation given AFAIK by Zadeh   
   himself. But strictly speaking it is not a definition of a *subset*. It is   
   a relation "is-a-subset-of" defined on fuzzy subsets of the same universal   
   set. It is even not a fuzzy relation, for it yields true or false. Yet it   
   is not useless. It plays a fundamental role! Just if you are accidentally   
   looking for a *fuzzy* inclusion relation to use it in propositions for   
   fuzzy inference, then it is not what you need.   
      
   As an intuitionist I am using: {pos(B|A),nec(B|A)} (see   
   http://www.dmitry-kazakov.de/ada/fuzzy.htm#fuzzy_proposition), but there   
   could be many other definitions, of course.   
      
   --   
   Regards,   
   Dmitry A. Kazakov   
   http://www.dmitry-kazakov.de   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)