 The fusion operators in the literature can be divided into two classes: syntax-based fusion and model-based fusion. The first type takes the propositional formulas as the information input, and typically considers the maximally consistent subsets of the belief profile. In a model-based operator, on the other hand, it is the interpretations of the formulas that are considered as inputs to the merging process. Hence, each belief base is seen as a set of models and the syntactic representation of its formulas is irrelevant. Recall the example we used at the beginning of  Section 2  to illustrate that the combination of belief bases is syntax-dependent. We had \(K_1 = \{a, b\}\), \(K_2 = \{a \wedge b\}\) and \(K_3 = \{\neg b\}\). A syntax-based fusion would treat \(a, b, a \wedge b, \neg b\) as inputs, whereas a model-based fusion would take \(mod(K_1) = mod(K_2) = \{(1, 1)\}\) and \(mod(K_3) = \{(1,0), (0,0)\}\). Since model-based operators have been applied to the problem of judgment aggregation, we will focus on that class of merging operators and refer to (Baral et al. 1992; Konieczny 2000; Grégoire and Konieczny 2006) for more on syntax-based fusion.