Interval hypermatrices (tensors) are introduced and interval α-hypermatrices are uniformly characterized using a finite set of'extreme'hypermatrices,where α can be strong P,semi-positive,or positive definite,among many others.It is shown that a symmetric interval is an interval (strictly) copositive-hypermatrix if and only if it is an interval (E)E0-hypermatrix.It is also shown that an even-order,symmetric interval is an interval positive (semi-)definite-hypermatrix if and only if it is an interval P (P0)-hypermatrix.Interval hypermatrices are generalized to sets of hypermatrices,several slice-properties of a set of hypermatrices are introduced and sets of hypermatrices with various slice-properties are uniformly characterized.As a consequence,several slice-properties of a compact,convex set of hypermatrices are characterized by its extreme points.