Mining Maximum Ordinal-Cardinal Consensus for Large-Scale Group Decision Making with Incomplete Fuzzy Preference Relations

In large-scale group decision-making (LSGDM), incomplete preferences often arise due to the complexity of LSGDM or the limited experience of decision-makers (DMs). When DMs provide preferences using incomplete fuzzy preference relations (IFPRs), most studies focus on cardinal information, overlooking the vital ordinal relations in IFPRs. However, a high level of cardinal consensus may not represent unanimous pairwise comparisons among DMs' preferences. In contrast, ordinal relations are crucial for ranking results by enabling pairwise comparisons. Therefore, this paper presents an LSGDM framework mining ordinal-cardinal group consensus by prioritizing ordinal relations followed by cardinal information of IFPRs. We begin by extracting ordinal relations from IFPRs. Next, an ordinal clustering optimization model is constructed to minimize overall conflicts. Finally, a value function-based consensus model is developed, identifying a consensus ranking by considering ordinal and cardinal information within subgroups. By linking this value function with IFPRs, each subgroup achieves a complete fuzzy preference relation (FPR) that is both ordinal and cardinal consistent. The application example shows the feasibility of this approach. Numerical analyses validate the clustering optimization model's effectiveness in reducing the global average conflict degree, and simulation studies with varying levels of incompleteness in FPRs demonstrate the consensus model's robustness in achieving consistent ranking results.