On Jun 17, 10:04 am, Aaron Brady <castiro...@gmail.com> wrote: snip > You (OP) may be interested in the definitions of the fuzzy operators: > > and( x, y ) := min( x, y ) > or( x, y ) := max( x, y ) > not( x ) := 1 (one)- x > nand( x, y ) := not( and( x, y ) ) = 1- min( x, y ) > > Defining 'xor' as '( x or y ) and ( not( x and y ) )', we have: > > xor( x, y ) := min( max( x, y ), 1- min( x, y ) ) > > However, defining 'xor' as '( x and not y ) or ( y and not x )', we > don't have: > > xor( x, y ) := max( min( x, 1- y ), min( y, 1-x ) )
Corollary: xor1( x, y ) === xor2( x, y ). Non-exhaustive demonstration, excerpt: >>> def xor1( x, y ): ... return min( max( x, y ), 1- min( x, y ) ) ... >>> def xor2( x, y ): ... return max( min( x, 1- y ), min( y, 1- x ) ) ... >>> for i in range( 0, 11, 2 ): ... for j in range( 0, 11, 2 ): ... print i, j, xor2( x, y )*10, ' ', ... print 0 0 0.0 0 2 2.0 0 4 4.0 0 6 6.0 0 8 8.0 2 0 2.0 2 2 2.0 2 4 4.0 2 6 6.0 2 8 8.0 4 0 4.0 4 2 4.0 4 4 4.0 4 6 6.0 4 8 6.0 6 0 6.0 6 2 6.0 6 4 6.0 6 6 4.0 6 8 4.0 8 0 8.0 8 2 8.0 8 4 6.0 8 6 4.0 8 8 2.0 10 0 10.0 10 2 8.0 10 4 6.0 10 6 4.0 10 8 2.0 They appear to be equal. I forgot to mention, fuzzy values take on values from the continuous open or closed range 0 to 1. -- http://mail.python.org/mailman/listinfo/python-list
