 An IC model-based fusion operator selects, among the models of the integrity constraints IC, those that are preferred, where the preference relation depends on the operator that is used. Thus, the collective belief set \(\Delta_{\IC}(E)\) is guaranteed to be a set of formulas that are true in all of the selected models and to satisfy the IC. In the example of the city council seen earlier, this means that building a playground and a parking lot will never be selected as a decision outcome. The preference information usually takes the form of a total pre-order (to recall, a pre-order is a reflexive and transitive relation) \(\le\) on the interpretations induced by a notion of distance d between an interpretation \(\omega\) and the profile E, denoted by \(d(\omega,E)\). Intuitively, this is to select a collective outcome that is the closest (with respect to some notion of distance to be specified) to all individual belief bases while satisfying the integrity constraints. It should be noted that a distance-based fusion operator does not always guarantee a unique result. We will come back to this point when we look at the application of belief merging to judgment aggregation.