This paper studies Lie superalgebras graded by an arbitrary set S (set grading). We show that the set-graded Lie superalgebra L decomposes as the sum of well-described set-graded ideals plus a certain linear subspace. Under certain conditions, the simplicity of L is characterized and it is shown that the above decomposition is exactly the direct sum of the family of its minimal set-graded ideals, each one being a simple set-graded Lie superalgebra.
