  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.
