Consensus reaching for ordinal classification-based group decision making with heterogeneous preference information

In group decision making (GDM), there may exist some problems that need to assign alternatives to some predefined ordered categories, which are called ordinal classification-based GDM problems. To obtain classification results that can be accepted by most decision makers (DMs), it is necessary to implement a consensus reaching process for ordinal classification-based GDM problems. In this paper, we study consensus reaching models for a new type of ordinal classification-based GDM problem, in which DMs do not provide criteria weights and category cardinalities but provide indirect and imprecise heterogeneous preference information. To do so, a consistency verification method is first proposed to check whether each DM’s preference information is consistent and then a minimum adjustment optimization model is developed to modify DMs’ inconsistent preference information. Afterwards, we establish some optimization models to obtain each DM’s possible categories for alternatives. Followed by this, we define the consensus levels of DMs and devise some optimization models to assist DMs in adjusting alternatives’ classification results and DMs’ preference information at the same time. Furthermore, a maximum support degree-based method is provided to determine the consensual classification result for alternatives. Finally, a numerical application and some sensitivity analysis are provided to justify the proposed models.