  The nonextensive statistics based on the $q$-entropy
$S_q=-\frac{\sum_{i=1}^v(p_i-p_i^q)}{1-q}$ has been so far applied to systems
in which the $q$ value is uniformly distributed. For the systems containing
different $q$'s, the applicability of the theory is still a matter of
investigation. The difficulty is that the class of systems to which the theory
can be applied is actually limited by the usual nonadditivity rule of entropy
which is no more valid when the systems contain non uniform distribution of $q$
values. In this paper, within the framework of the so called incomplete
information theory, we propose a more general nonadditivity rule of entropy
prescribed by the zeroth law of thermodynamics. This new nonadditivity
generalizes in a simple way the usual one and can be proved to lead uniquely to
the $q$-entropy.
