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 ${\mathrm{\Delta }}^n$ 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 ${\lambda }_{m+1}\le {\lambda }_m+1,{\lambda }_1=1,{\lambda }_m\to \mathrm{\infty }(m\to \mathrm{\infty })$. We prove completeness properties of these spaces. Further, we investigate some inclusion relations related to these spaces.