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The concepts of intuitionistic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and UP (BCC)-filters of UP (BCC)-algebras are presented, some of their features are explained, and their extensions are demonstrated using the theory of hesitant fuzzy sets as a foundation. The necessary conditions for those intuitionistic hesitant fuzzy sets are provided and include their relation to their complement. The concept of prime and weakly prime of intuitionistic hesitant fuzzy sets was also introduced and studied. We also talk about the connections between intuitionistic hesitant fuzzy UP (BCC)-subalgebras (UP (BCC)-ideals, UP (BCC)-filters) and their level subsets. The homomorphic pre-images of intuitionistic hesitant fuzzy UP (BCC)-filters in UP (BCC)-algebras are also studied and some related properties are investigated.