  The necessary information for specifying a complex system may not be
completely accessible to us, i.e., to mathematical treatments. This is not to
be confounded with the incompleteness of our knowledge about whatever systems
or nature, since here information is our ignorance. In conventional statistics
and information theories, this information or ignorance is supposed completely
accessible to theoretical treatments connected with complete probability
distributions. However, the hypothesis of incomplete information supposes that
the information of certain systems can be incomplete as calculated in the usual
way as in the conventional information theories. This hypothesis has been used
in order to generalize the conventional statistics theory. The generalized
statistics and information theory characterized by an empirical parameter has
been proved useful for the formulation of the nonextensive statistical
mechanics based on Tsallis entropy, for the description of some correlated
quantum systems and for the derivation of the stationary probability
distributions of nonequilibrium complex systems evolving in hierarchical or
fractal phase space. In this paper, the incompleteness of the information will
be discussed from mathematical, physical and epistemological considerations
with an example of information calculation in fractal phase space with
stationary probability distribution.
