  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.
