中文摘要：

Vague集是fuzzy集的推广,但是与fuzzy集不同的是,它同时提供支持和反对的证据.因此,Vague集的模糊熵应该既有Vague集的未知性又有fuzzy集的不确定性.提出了一个考虑未知性和不确定性因素的Vague集模糊熵的公理化定义,给出一种新的Vague集模糊熵计算公式,得到了新的Vague熵一些良好的数学性质.通过定理证明和实例分析,表明新公式的定义是合理的.

英文摘要：

Vague sets are one of generalizations of fuzzy sets.But Vague sets are very different from fuzzy sets,it presents favoring and opposing evidence simultaneously.So,the fuzzy entropy of Vague sets should include the unknown and the uncertainty.Proposed an improved axiom definition of the fuzzy entropy of Vague sets,the axiom definition take into account the unknown and the uncertainty.And a corresponding new formula of the fuzzy entropy of Vague sets was presented,obtained some good mathematical nature of the new formula.By proved theorem and analyzed example,it shows that the new formula is rational.