Soft set theory serves as a mathematical framework for handling uncertain information, and hesitant fuzzy sets find extensive application in scenarios involving uncertainty and hesitation. Hesitant fuzzy sets exhibit diverse membership degrees, giving rise to various forms of inclusion relationships among them. This article introduces the notions of hesitant fuzzy soft $\beta$-coverings and hesitant fuzzy soft $\beta$-neighborhoods, which are formulated based on distinct forms of inclusion relationships among hesitancy fuzzy sets. Subsequently, several associated properties are investigated. Additionally, specific variations of hesitant fuzzy soft $\beta$-coverings are introduced by incorporating hesitant fuzzy rough sets, followed by an exploration of properties pertaining to hesitant fuzzy soft $\beta$-covering approximation spaces.

翻译：软集理论是处理不确定性信息的数学框架，犹豫模糊集在涉及不确定性和犹豫的场景中广泛应用。犹豫模糊集具有多种隶属度，由此衍生出它们之间不同类型的包含关系。本文基于犹豫模糊集之间的不同包含关系形式，引入了犹豫模糊软β-覆盖与犹豫模糊软β-邻域的概念。随后，研究了若干相关性质。此外，通过融入犹豫模糊粗糙集，引入了犹豫模糊软β-覆盖的特定变体，并进一步探讨了犹豫模糊软β-覆盖近似空间的相关性质。