<p>In this paper, we propose Pareto Z-eigenvalue inclusion intervals of tensor Z-eigenvalue complementarity problems and the corresponding sufficient criteria for the copositivity of tensors, which only depend on the negative entries and Z-diagonal entries of tensors. Based on these inclusion intervals, upper and lower bounds for the Pareto Z-eigenvalues of tensors are presented. The relationships between these localization sets are obtained. Finally, some sufficient conditions for the solution existence of the TCP and TGEiP are presented, and these conditions are also used to test the vacuum stability of a general scalar potential.</p>