 We can now define the distance between an interpretation \(\omega\) and a belief profile E, which is needed for the second step. We need an aggregation function \(D: R^{+n} \rightarrow R^{+}\) that takes the distances between the models of IC and the belief bases \(K_i\) calculated in the first step, and aggregate them into a collective distance. This is: \(D(\omega, E) = D(d(\omega, K_1)\), \(d(\omega, K_2)\), \(\ldots\), \(d(\omega, K_n))\). A total pre-order over the set W of all interpretations is thus obtained. The merging operator can now select all interpretations that minimize the distance to the profile E.