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. Generalized uncertain theory: concepts and fundamental principles