Ordinal consensus measure with objective threshold for heterogeneous large-scale group decision making

Because of the increasing complexity of real-world decision-making environment, there is a trend that a large number of decision-makers are becoming involved in group decision making problems. In large-scale group decision making problems, owing to various backgrounds and psychological cognition, it is natural to use heterogeneous representation forms (quantitative or qualitative) to express distinct preference information for different decision-makers. In this paper, we investigate the consensus reaching process in the environment of heterogeneous large-scale group decision making. A novel ordinal consensus measure with an objective threshold based on preference orderings is proposed. This process contains five parts: (1) obtaining ordinal preferences; (2) classifying all decision-makers into several subgroups using the ordinal k-means clustering algorithm; (3) measuring consensus levels of subgroups and the global group using novel ordinal consensus indexes; (4) providing suggestions for decision-makers to revise preferences using feedback strategies; (5) obtaining final decision result. An illustrative example is provided to verify the implementation of the proposed consensus model. Lastly, we discuss the approaches to determine the appropriate number of clusters and the initialization center points for the proposed ordinal k-means clustering algorithm.