<p>The max-plus algebra of interval tensors provides a framework for extending interval linear systems to interval multi-linear systems. In this work, we introduce and analyze the notions of solvable interval, solvable entry, and subsolvable entry of such systems. By establishing fundamental theoretical properties, we investigate the intricate relationships among strong solvability, extremal solvability, and strong subsolvability in interval multi-linear systems within max-plus algebra. Our findings offer a deeper understanding of the solvability structure in these systems and lay the groundwork for further advancements in tensor-based max-plus analysis. We validate these concepts through numerical experiments, including high-dimensional tensor systems and a real-world problem, demonstrating the robustness and scalability of our approach in practical settings.</p>