In this paper, we introduce the concept of (alpha,beta)-fuzzy interior ideals and discuss some fundamental properties of (alpha,beta)-fuzzy interior ideals. Alpha and beta will denote any one of ∈, q(λ,μ),∈∨q(λ,μ) or ∈∧q(λ,μ) with α≠∈∧q(λ,μ) unless otherwise specified. When λ=0,μ=0.5, we can get corresponding results in Jun and Song [Y. B. Jun, S. Z. Song, Generalized fuzzy interior ideals in semi groups, Inform. Sci. 2006, 176: 3079-3093]. When λ=0,μ=1, we can get the common results.