In this article we prove the strict monotonicity of the spectral radius of weakly irreducible nonnegative tensors. As an application, we give a necessary and sufficient condition for an interval hull of tensors to be contained in the set of all strong $\mathcal{ M}$-tensors. We also establish some properties of $\mathcal{ M}$-tensors. Finally, we consider some problems related to interval hull of positive (semi)definite tensors and $P(P_0)$-tensors.
Categories: math.SP