Ordinal-cardinal consensus analysis for large-scale group decision making with uncertain self-confidence

Consensus analysis is necessary for large-scale group decision making (LSGDM) for ensuring reasonable decision results. This paper offers a new method for LSGDM with uncertain self-confidence that follows ordinal-cardinal consensus analysis. For this purpose, a new interval ranking method is first proposed to compare alternatives. Then, an improved ordinal clustering method on criteria is introduced using the deviation between individual ranking positions. In view of opinion deviation, uncertain self-confidence deviation, and ranking deviation, the weights of decision makers (DMs) are defined. Similarly, the weights of clusters are determined by further combining cluster cardinality. Further, an ordinal-cardinal consensus procedure is offered, which contains two algorithms: the first algorithm is about the ordinal consensus improvement in view of three aspects: ranking adjustment, opinion adjustment, and uncertain self-confidence; the second algorithm studies the cardinal consensus improvement under the ordinal consensus requirement, which also mainly contains three aspects: opinion adjustment, the number of adjusted judgments, and uncertain self-confidence. Moreover, a new algorithm for LSGDM is presented. Finally, an example is provided to check the feasibility and efficiency of the new method, and a comparison analysis is also made.