Foundational propositions of hesitant fuzzy soft $β$-covering approximation spaces
Shizhan Lu
TL;DR
The paper addresses uncertainty-imbued information by extending rough-set theory with hesitant fuzzy sets through the introduction of hesitant fuzzy soft $β$-coverings and $β$-neighborhoods. It defines six variants of $β$-neighborhoods and six corresponding $β$-covering based approximation spaces, enabling six corresponding lower/upper rough approximations within hesitant fuzzy soft contexts. The work establishes inclusion, complement, and algebraic properties of these structures, and demonstrates how to construct and relate $pβ$-, $aβ$-, $mβ$-, $sβ$-, $tβ$-, and $nβ$-coverings and neighborhoods to form a comprehensive framework for covering-based rough sets under hesitation. This contributes a foundational mathematical model for nuanced, uncertain data analysis in decision-making and related domains, with potential applications in filtering, clustering, and information retrieval where hesitation plays a central role.
Abstract
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.