Linguistic multiperson decision making based on the use of multiple preference relations

In multiperson decision making situations, it is quite natural that different decision makers who may have different background and knowledge will provide their preferences by different kinds of preference relations. This paper proposes a linguistic multiperson decision making model (LMDMM) based on linguistic preference relations, integrating fuzzy preference relations, different types of multiplicative preference relations and multigranular linguistic preference relations. In the LMDMM, several transformation functions are first obtained to relate fuzzy preference relations and different types of multiplicative preference relations with multigranular linguistic preference relations. Then, we design the selection process of the LMDMM, based on the use of the fuzzy majority and the extended ordered weighted averaging operator (or the 2-tuple ordered weighted averaging operator), and discuss conditions under which the proposed selection process satisfies the social choice axioms. At last, we analyze the internal consistency of the proposed transformation functions. The results in this paper are helpful to complete Chiclana et al.'s fuzzy decision model [Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations, Fuzzy Sets and Systems 97 (1998) 33–48].