Abstract: The fuzzy entropy of vague sets should include the unknown and the uncertainty. At first, a counterexample is given to show that the result used the present method in some cases and real conclusions are contrary, then an improved axiom definition of the fuzzy entropy of vague sets that taking really into account two factors is proposed, and a corresponding new formula of the fuzzy entropy of vague sets is presented. Finally it really taking into account simultaneously the unknown and the uncertainty is pointed out by proved theorem and analyzed example, and then it is proved that the definition of the fuzzy entropy of vague sets is more efficient and rational.

Key words: fuzzy entropy, uncertainty, Vague sets, Fuzzy sets, membership function

摘要： 对于Vague集模糊熵应该既有Vague集的未知性又有Fuzzy集的不确定性。首先在给出了反例证实现有方法在某些情况得出的结果与实际结论不一致情况下，提出了一个真正考虑了两种因素的改进的Vague集模糊熵公理化定义，然后给出一种Vague集模糊熵的新计算公式，最后通过定理证明和实例分析，指出它确实同时考虑到Vague集的未知性和不确定性，从而证明所给出Vague集模糊熵的定义是更加合理的。

关键词: 模糊熵, 不确定性, Vague集, Fuzzy集, 隶属函数