中文摘要：

信息粒和粗糙熵作为研究信息系统不确定性问题的两种主要方法,已被广泛应用于许多领域。本文基于区间值犹豫模糊二元关系,给出了区间值犹豫模糊粒度结构概念和区间值犹豫模糊粒的基数概念,讨论了区间值犹豫模糊粒度结构上的三种偏序关系。在区间值犹豫模糊粒度结构基础上给出了区间值犹豫模糊信息粒度和粗糙熵的概念,讨论了区间值犹豫模糊信息粒度和粗糙熵的偏序关系,分析了区间值犹豫模糊信息粒度和粗糙熵与已有信息粒度和粗糙熵之间的关系,并通过实例验证了有关定义和定理的正确性。

英文摘要：

Information granulation and rough entropy as the two main approaches for investigating the uncertainty of information systems have been widely employed in many domains.In the paper,the concepts of interval-valued hesitant fuzzy granular structures and the cardinalities of interval-valued hesitant fuzzy granularity are given base on the interval-valued hesitant fuzzy binary relation,three new partial order relations in interval-valued hesitant fuzzy granular structures are discussed.The concepts of information granularities and rough entropy in interval-valued hesitant fuzzy granular structures are given,and their partial orders are discussed,the relationships between the intervalvalued hesitation fuzzy information granularities and interval-valued hesitant fuzzy rough entropy and all kinds of related information granularities and rough entropy that already exist are analyzed.In addition,an example is provided to show the validity of the related definitions and theorems.