An ideal $I$ is a family of subsets of positive integers $\mathbb N$ which is closed under taking finite unions and subsets of its elements. In this paper, using $\lambda$-ideal convergence as a variant of the notion of ideal convergence, the difference operator $\Delta^n$ and Musielak–Orlicz functions, we introduce and examine some generalized difference sequences of interval numbers, where $\lambda=(\lambda_m )$ is a nondecreasing sequence of positive real numbers such that $λ_{m+1}\le \lambda_m +1,\lambda_1=1,\lambda_m \to \infty~(m\to \infty)$. We prove completeness properties of these spaces. Further, we investigate some inclusion relations related to these spaces.