Large-scale group decision-making with incomplete fuzzy preference relations: The perspective of ordinal consistency

Incomplete preferences have become increasingly common in light of the redundancy of information and time-related pressures. Incomplete fuzzy preference relations (IFPRs) have thus attracted considerable research interest in recent years. A number of relevant studies have tended to rely on the cardinal consistency of a single IFPR or an aggregated group of preference relations. However, the preference-related information on which the final decision relies may be not reliable because ordinal inconsistency might persist following the application of cardinal consistency or an improvement in consensus. This paper proposes an optimization model that considers both cardinal consistency and ordinal consistency to estimate unknown preferences in IFPRs. The authors develop a model to optimize the consensus in problems involving large-scale group decision-making by using IFPRs. The proposed model can explicitly control ordinal consistency, minimize the extent of requisite modifications to the preferences, and guarantee that the cardinal and ordinal consistencies are well managed when a predefined level of consensus has been achieved to a greater extent than prevalent approaches to estimate unknown preferences. The individual and group FPRs revised by using the proposed model are more reliable as they contain no contradictory elements. Several classical numerical examples are used to verify the superiority of the proposed model to those currently used in the area.