Two Z-eigenvalue inclusion theorems for tensors presented by Wang et al. (Discrete Cont. Dyn.-B, 2017, 22(1): 187–198) are first generalized to E-eigenvalue inclusion theorems. And then a tighter E-eigenvalue inclusion theorem for tensors is established. Based on the new set, a sharper upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to verify the theoretical results