The notions of hesitant fuzzy translations and hesitant fuzzy extensions of a hesitant fuzzy set on BCK/BCI-algebras are introduced, and related properties are investigated. We prove that every hesitant fuzzy translation of a hesitant fuzzy subalgebra (ideal) is a hesitant fuzzy subalgebra (ideal). Conditions for a hesitant fuzzy set to be a hesitant fuzzy subalgebra (ideal) are provided. We show that if a hesitant fuzzy set is a hesitant fuzzy subalgebra (ideal), then its support is a subalgebra (ideal), and also prove that if the support of a hesitant fuzzy set is a subalgebra (ideal), then its hesitant fuzzy translation is a hesitant fuzzy subalgebra (ideal).
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