The authors present a new definition of interval arithmetic operations. They argue that these operations are superior to the classical ones as they may end up with lesser widths; however, the basic property that \(\alpha\in{\mathbf a}\), \(\beta\in{\mathbf b}\) imply \(\alpha\circ\beta\in {\mathbf a}\circ {\mathbf b}\) for any \(\circ\in\{+,-,*,/\}\) seems not to hold. Furthermore, they define an interval order \({\mathbf a}\preceq{\mathbf b}\) if either \(\text{mid}({\mathbf a})<\text{mid}({\mathbf b})\), or \(\text{mid}({\mathbf a})=\text{ mid}({\mathbf b})\) and \(\text{ rad}({\mathbf a})\geq\text{ rad}({\mathbf b})\), and they show that it forms a partial ordering on the set of real intervals.