Abstract
In this paper, the concept of interval-valued intuitionistic fuzzy set to UPsubalgebras and UP-ideals of UP-algebras are introduced. Relations among IVIF UPsubalgebras with IVIF UP-ideals of UP-algebras are investigated. The homomorphic image and inverse image of IVIF UP-subalgebras and IVIF UP-ideals are studied and some related properties are investigated. Equivalence relations on IVIF UP-ideals are discussed. Also, the product of IVIF UP-algebras are investigated.