interval $r$-tensor

First, we define and investigate some new classes of interval tensors, called interval exceptionally regular tensors  ($ER-$tensor) and interval $wP-$tensors which is relevant to interval strictly semi-positive tensors. Also, we show that $ER-$tensor is a wide class of interval tensors, which includes many important structured tensors. Second, some classes of interval matrices are extended to interval tensors, such as interval $R(R_0)$-tensor and column sufficient interval tensor. We discuss their relationships with interval positive semi-definite tensors and some other structured interval tensors. In addition,  necessary and sufficient conditions for interval (strictly) copositive and interval $E_0$-tensors are presented and investigated. Finally, we extend the concept of the column sufficient interval matrix to the column sufficient interval tensor.