Order-of-magnitude models in qualitative reasoning are basic theoretical tools to model real-world problems in which only incomplete qualitative knowledge is available. In this paper, we introduce interval-valued fuzzy sets into order-of-magnitude qualitative reasoning, generalizing the order-of-magnitude spaces of both qualitative labels and fuzzy-qualitative labels. We present a new lattice structure of linguistic descriptions in an interval-valued fuzzy framework, and introduce the interval-valued fuzzy-qualitative labels as interval-valued fuzzy sets with certain requirements. We define two operations related to the inclusion in the set of interval-valued fuzzy-qualitative labels. The set of interval-valued fuzzy-qualitative labels is structured as a lattice with these two operations.