AbstractThis paper aim is to apply the notions of the intersection and the union of any fuzzy set to UP-algebras. We investigate properties of the intersection and the union of T-fuzzy UP-subalgebras, T-fuzzy near UP-filters, T-fuzzy UP-filters, T-fuzzy UPideals, T-fuzzy strongly UP-ideals, anti-T-fuzzy UP-subalgebras, and anti-T-fuzzy near UP-filters of UP-algebras.