犹豫模糊集的熵

Entropy Measure for Hesitant Fuzzy Sets

结合犹豫模糊集自身的模糊性和犹豫性特征，研究犹豫模糊集的熵公理化定义和熵公式．先对犹豫模糊值提出了熵公理化定义和熵公式，在此基础上，定义犹豫模糊集的熵公理化定义和熵公式，从而完善犹豫模糊集的熵理论．最后，将提出的犹豫模糊值的熵公理化定义和熵公式与现有文献中的相关定义进行比较，结果表明所提的熵公式既能反映犹豫模糊值的模糊性，又能反映其犹豫性，具有更强的区分犹豫模糊值不确定性的能力．

In this paper, we study the axiomatic definition of entropy and the entropy measure for hesitant fuzzy sets （HFSs） in accordance to fuzziness and hesitation respectively. Firstly, we propose the axiomatic definition of entropy and an entropy measure for hesitant fuzzy elements （HFEs）. Then, we present the axiomatic definition of entropy and entropy measure for HFSs in order to perfect the entropy theory of HFSs. At last, we give the comparison between the proposed theory and relevant definitions in the existing literatures. The result shows that the proposed entropy measure can not only consider the fuzziness of HFEs but also the hesitation of HFEs, hence, the proposed entropy measure can distinguish the degree of uncertainty for HFEs more effectively.