In this paper, we introduce the notions of Q-fuzzy UP-ideals and Q-fuzzy UP-subalgebras of UP-algebras, and their properties are investigated. Relations between a Q-fuzzy UP-ideal (resp. Q-fuzzy UP-subalgebra) and a level subsets of a Q-fuzzy set are investigated, and conditions for a Q-fuzzy set to be a Q-fuzzy UP-ideal (resp. Q-fuzzy UP-subalgebra) are provided. Finally, prove that it is not true that if µ·δ is a Q-fuzzy UP-ideal (resp. Q-fuzzy UP-subalgebra) of A×B, then either µ is a Q-fuzzy UP-ideal (resp. Q-fuzzy UP-subalgebra) of A or δ is a Q-fuzzy UP-ideal (resp. Q-fuzzy UP-subalgebra) of B.
