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The concept of hesitant union (⋓) is introduced. Using this, the notions of⋓-hesitant fuzzy subalgebras and⋓-hesitant fuzzy ideals are introduced and several properties are investigated. Relations between∪-hesitant fuzzy subalgebras (resp. ideals) and⋓-hesitant fuzzy subalgebras (resp. ideals) are considered. Relations between a⋓-hesitant fuzzy subalgebra/ideal and its lower level set are investigated. Characterizations of∪-hesitant fuzzy subalgebras/ideals are discussed. Given a subalgebra (resp., ideal) A of a BCK/BCI-algebra X, a⋓-hesitant fuzzy subalgebra (resp., ideal) is established.