Abstract: Based on the theory?of hesitant fuzzy granularity structure, combined with the concepts of Shannon’s entropy and the new entropy introduced by Liang, the concepts of type[Ι]and type[Π]hesitant fuzzy information entropy, joint entropy, condition entropy are given. The partial order of hesitant fuzzy-information entropy is discussed, the relationships between?the hesitation fuzzy information entropy, joint entropy, condition entropy presented above and all kinds of related entropy that?already?exist are analyzed.

Key words:  hesitant fuzzy granular structure, hesitant fuzzy information entropy, hesitant fuzzy information joint entropy, hesitant fuzzy information condition entropy

摘要： 基于犹豫模糊粒度结构理论，结合Shannon熵和梁吉业等人提出的新熵概念，给出[Ι]型和[Π]型犹豫模糊信息熵、联合熵、条件熵概念，讨论了两类犹豫模糊信息熵的偏序性，分析了给出的犹豫模糊信息熵、联合熵、条件熵与已存在的各类相关熵之间的关系。

关键词: 犹豫模糊粒度结构, 犹豫模糊信息熵, 犹豫模糊信息联合熵, 犹豫模糊信息条件熵