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Multiperson decision making (MPDM) models with heterogeneous preference representation structures have initiated by Chiclana et al. In this study, we propose a novel framework for MPDM problems with heterogeneous preference representation structures. This framework takes the decision makers’ psychological behaviors into consideration and is based on the prospect theory, which is one of the most influential psychological behavior decision theories. In this framework, the heterogeneous preference representation structures are all transformed into preference orderings. The preference-approval structures are introduced to determine the reference points in prospect theory, and then the prospect value function is used to obtain individual and collective prospect values. Finally, based on the prospect values and preference-approval structures, we propose the two-step feedback adjustment rules, which will …