Consensus modeling with interactive utility and partial preorder of decision-makers, involving fairness and tolerant behavior

Abstract

Reaching consensus in group decision-making (GDM) is usually achieved by minimizing opinion deviation (distance) or maximizing the utility of the group in traditional mathematical modeling. While the former ignores the preferences (individual values) of decision-makers (DMs), the latter is most often based on the implicit assumption that DMs are mutually independent, which results in the loss of a large amount of decision-making information about the actual interactions between DMs. Moreover, numerous studies on GDM did not pay enough attention to individual participation and satisfaction in the decision-making process. To overcome these defects, in this paper, we construct a new kind of consensus models for group utility optimization. We employ 2-additive Choquet integral to aggregate the utilities of individual DMs interacting pairwise. Linear programming is used to learn fuzzy measures (weights) that are consistent with a partial preorder of DMs. Moreover, we describe the coordinator's fairness preference and tolerant behavior with the help of Gini coefficient and orness operator, thus exploring the impacts of coordinator's psychological behaviors on consensus reaching. The orness operator of the Choquet integral is generalized to a particularly useful 2-additive form with Möbius representation. Finally, a comparative and parametric analysis is performed to illustrate and validate the proposed models on a case study concerning the price negotiation of medical insurance drugs.