 Another interesting construction is to assign to each alternative an interval instead of a single number. This requires two real-valued functions, \(u_{max}\) and \(u_{min}\), such that for all \(A, u_{max}(A)\ge u_{min}(A)\). Here, \(u_{max}(A)\) represents the upper limit of the interval assigned to \(A\), and \(u_{min}(A)\) its lower limit. \(A \succ B\) holds if and only if all elements of the interval assigned to \(A\) have higher value than all elements of the \(B\) interval: