Afraid so: The OR of two objects is at least as "big" as either
thing OR'ed. An easy way to write it is
(X OR Y) >= MAX(X, Y)
The above recalls the fact that the MAX operator is the smallest
of all "t-conorms", the usual choices for disjunction (OR). Dually,
it is the case that
(X AND Y) <= MIN(X, Y)
which says that among all "t-norms" (AND-operators), MIN is the largest.
Thus MIN and MAX are a distinguished t-norm/t-conorm pair: they are the
*extremal* objects. (Between them lie the *weighted averages*, usually
represented as integrals.)
(In the above, the inequalities are *pointwise*; the fuzzy sets X and Y
are *functions* from some universe into the unit interval [0, 1].)
Noise about t-norms/t-conorms aside, you simply had the key relationship
backwards.
Exercise: Show that 0 <= x + y - xy <= 1 for all x,y in [0, 1].
Fred A Watkins, Ph.D.
HyperLogic Corporation
PO Box 300010
Escondido, CA 92030-0010 USA
voice: +1 760 746 2765 x 9117
fax: +1 760 746 4089
email: fwatkins@hyperlogic.com