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In this paper, we present four categories of covering-based intuitionistic hesitant fuzzy rough set (CIHFRS) models using intuitionistic hesitant fuzzy β -neighborhoods (IHF β -neighborhoods) and intuitionistic hesitant fuzzy complementary β -neighborhoods (IHFC β -neighborhoods. Through theoretical analysis of covering-based IHFRS models, we propose the intuitionistic hesitant fuzzy TOPSIS (IHF-TOPSIS) technique for order of preference by similarity to an ideal solution, addressing multicriteria decision-making (MCDM) challenges concerning the assessment of IHF data. A compelling example aptly showcases the suggested approach. Furthermore, we address MCDM problems regarding the assessment of IHF information based on CIHFRS models. Through comparison and analysis, it is evident that addressing MCDM problems by assessing IHF data using CIHFRS models proves more effective than utilizing intuitionistic fuzzy data with CIFRS models or hesitant fuzzy information with CHFRS models. IHFS emerges as a unique and superior tool for addressing real-world challenges. Additionally, covering-based rough sets (CRSs) have been successfully applied to decision problems due to their robust capability in handling unclear data. In this study, by combining CRSs with IHFS, four classes of CIFRS versions are established using IHF β -neighborhoods and IHFC β -neighborhoods. A corresponding approximation axiomatic system is developed for each. The roughness and precision degrees of CBIHFRS models are specifically talked about. The relationship among these four types of IHFRS versions and existing related versions is presented based on theoretical investigations. A method for MCDM problems through IHF information, namely, IHF-TOPSIS, is introduced to further demonstrate its effectiveness and applicability. By conducting a comparative study, the effectiveness of the suggested approach is evaluated. [ABSTRACT FROM AUTHOR]