Modeling the Social Influence in Consensus Reaching Process with Interval Fuzzy Preference Relations

Abstract

Consensus process plays a prominent role in decision-making problems. In traditional way, experts with low consensus degree are asked to modify their opinions according to the given advices. However, in fact, experts neither simply adopt nor completely ignore the opinions of others. In general, experts will refer to other experts’ opinions to a certain extent and their opinions will evolve due to their interactions. The aim of this paper, therefore, is to propose a consensus model based on uncertain opinion evolution to model the influence between experts during the negotiation and communication process. Firstly, we construct an influence network among experts by taking both objective similarity degree and some subjective psychological traits into consideration. Secondly, a consensus model based on opinion evolution with interval fuzzy preference relations (IFPRs) is proposed. After identifying the incompatible preference with lower consensus degree, experts will modify their preferences according to the preference evolution under the influence network. Then, we prove that the reciprocity property maintains through the dynamic consensus reaching process, and a sufficient condition guaranteeing that the consensus can be reached in the influence network is derived. Furthermore, two nonlinear programming models are proposed to justify whether the IFPR satisfies the acceptable consistency and to calculate the priority vector of the IFPR, respectively. Finally, a case study and comparative analysis are made to illustrate the effectiveness of the proposed model.