Multiperson decision making with different preference representation structures: A direct consensus framework and its properties

This study proposes a direct consensus framework for multiperson decision making (MPDM) with different preference representation structures (preference orderings, utility functions, multiplicative preference relations and fuzzy preference relations). In this framework, the individual selection methods, associated with different preference representation structures, are used to obtain individual preference vectors of alternatives. Then, the standardized individual preference vectors are aggregated into a collective preference vector. Finally, based on the collective preference vector, the feedback adjustment rules, associated with different preference representation structures, are presented to help the decision makers reach consensus. This study shows that the proposed framework satisfies two desirable properties: (i) the proposed framework can avoid internal inconsistency issue when using the transformation functions among different preference representation structures; (ii) it satisfies the Pareto principle of social choice theory. The results in this study are helpful to complete Chiclana et al.’s MPDM with different preference representation structures.