  Although there are many mathematical theories to address uncertain phenomena
however, these theories are presented under implicit presupposition that
uncertainty of objects is accurately measurable while not considering that the
measure of uncertainty itself may be inaccurate. Considering this evident but
critical overlook, on the basis of reviewing and commenting several widely used
mathematical theories of uncertainty, the fundamental concepts and axiomatic
system of generalized uncertain theory (GUT)are proposed for the purpose of
describing and analyzing that imprecision of objects has inaccurate attributes.
We show that current main stream theories of studying uncertain phenomena, such
as probability theory, fuzzy mathematics, etc., are the special cases of
generalized uncertain theory. So the generalized uncertain theory could cover
previous main stream theories of studying uncertainty. Further research
directions and possible application realms are discussed. It may be a
beneficial endeavor for enriching and developing current uncertainty
mathematical theories.
