In this chapter, the authors introduce the concepts of (∈,∈∨qkδ)-fuzzy interior ideal in semigroup, which is a generalisation of (∈,∈∨qk)-fuzzy interior ideal and (∈,∈∨q)-fuzzy interior ideal in semigroup, and investigate some of its properties. They give example to show that (∈,∈∨qkδ)-fuzzy interior ideal in semigroup is not an (∈,∈∨qk)-fuzzy interior ideal and (∈,∈∨q)-fuzzy interior ideal in semigroup. They show that every (∈,∈∨qkδ)-fuzzy ideal is an (∈,∈∨qkδ)-fuzzy interior ideal, but the converses are not true in general.