The essential role of the particular families of capacities and the capacity identification methods is to help the decision maker to deal with the exponential complexity inherent in the construction process of the capacity. The 2-additive capacities appear to be the most popular among the particular families of capacities since they permit to model interactions between criteria while preserving simplicity. Besides the preference with respect to the decision criteria, most of the capacity identification methods also need to provide the desired overall evaluations of the decision alternatives in the learning set, which is a time-consuming task for the decision maker. In this paper, we propose some models to identify 2-additive capacities only from a kind of refined preference information with respect to the decision criteria called the multicriteria correlation preference information (MCCPI). The MCCPI is a group of 2-D preference information which can be described and obtained by the refined diamond diagram. The common principle of the proposed models is to minimize the different kinds of deviations between the MCCPI and the most desired 2-additive capacity(ies). A multicriteria decision making example is presented to show the feasibility of the proposed methods, and a 2-D scale of the MCCPI is also introduced in the further discussion of the illustrative example.