By a semantic analysis to the uncertainty measure of rough set, an improved axiomatic definition of the uncertainty measure for the rough set is proposed. Firstly, based on the analysis of mathematical characters of axiomatic definition, two new uncertainty measures based on conditional possibility are proposed. Then, it is proved that they are the uncertainty measures under the axiomatic definition, and the corresponding uncertainty measuring formulas of knowledge are derived, respectively. It is found that one of them is just the existing conditional information entropy, the other has a complement relationship with the certainty measure. An example is given to compare the uncertainty measures, which illustrates that the proposed formulas are consistent with the semantics of uncertainty for the rough set.