Foundational propositions of hesitant fuzzy soft $β$-covering approximation spaces
This work provides incremental theoretical foundations for soft set theory in uncertainty modeling, primarily relevant to researchers in fuzzy mathematics and decision-making under hesitation.
The paper tackles the problem of handling uncertain information by introducing hesitant fuzzy soft β-coverings and neighborhoods based on inclusion relationships among hesitant fuzzy sets, and investigates their properties and variations with hesitant fuzzy rough sets.
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 $β$-coverings and hesitant fuzzy soft $β$-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 $β$-coverings are introduced by incorporating hesitant fuzzy rough sets, followed by an exploration of properties pertaining to hesitant fuzzy soft $β$-covering approximation spaces.