关于Vague集的模糊熵

On the Fuzzy Entropy of Vague Sets

由于Vague集是Zadeh's模糊集的一个扩展,为计算Vague集的模糊熵,有学者提出将Vague集转化为模糊集,然后借用模糊集有关熵的计算方法来讨论它们。该文首先给出反例说明Li's(2003)的方法在某些情况下和基于模糊集的Vague集模糊熵定义不一致。在指出Vague集的模糊性主要来自未知信息和不确定性信息的基础上,提出了一个基于非模糊集的Vague集模糊熵公理化定义,给出了该类模糊熵的计算公式,最后通过定理证明了它确实同时考虑到了影响Vague集模糊熵的两个因素。

Since Vague sets are one of generalizations of Zadeh＇s fuzzy sets,some researchers have proposed to transform them into fuzzy sets and measure their fuzzy information by related methods of fuzzy sets.At first,some counterexamples are given to show that Li＇s （2003） methods are not valid in some cases.It＇s pointed out that the fuzziness of Vague sets mainly comes from unknown and uncertainty information.Then an axiom definition of the entropy of Vague sets based on non-fuzzy sets is proposed and a corresponding formula is presented.Finally a theorem proves that the formula actually takes the two factors into account simultaneously.