The idea of inf at -hesitant fuzzy UP-subalgebras (inf at-HFUPSs) (resp., UP-filters (UPFs), UP-ideals (UPIs), strong UP-ideals (SUPIs)) is presented, various facts are proven, and the generalizations of these hesitant fuzzy sets (HFSs) are addressed. This concept is a generalization of interval-valued fuzzy UPSs (IvFUPSs) (resp., UPFs, UPIs, SUPIs) of UP-algebras. In addition, we analyze the relationships between the level subsets of the  inf-hesitant fuzzy UPSs (inf-HFUPSs) (resp., UPFs, UPIs, SUPIs). Finally, characterizations of  inf-HFUPSs (resp., UPFs, UPIs, SUPIs) are examined in terms of fuzzy sets (FSs), Pythagorean fuzzy sets (PFSs), HFSs, interval-valued fuzzy sets (IvFSs), and cubic sets (CSs).