Using the hesitant intersection (⋒), the notions of ⋒-hesitant fuzzy subalgebras, ⋒-hesitant fuzzy ideals and ⋒-hesitant fuzzy p-ideals are introduced, and their relations and related properties are investigated. Conditions for a ⋒-hesitant fuzzy ideal to be a ⋒-hesitant fuzzy p-ideal are provided. The extension property for ⋒-hesitant fuzzy p-ideals is established.

Keywords: Hesitant intersection, Hesitant fuzzy subalgebra, Hesitant fuzzy ideal, , Hesitant fuzzy $p$-ideal.