Managing consensus and self-confidence in multiplicative preference relations in group decision making

Preference relations have been widely used in Group Decision Making (GDM) to represent decision makers’ preferences over alternatives. Recently, a new kind of preference relation called the self-confident multiplicative preference relation has been presented, which is formed considering multiple self-confidence levels into the multiplicative preference relation. This paper proposes an iteration-based consensus building framework for GDM problems with self-confident multiplicative preference relations. In this consensus building framework, an extended logarithmic least squares method is presented to derive the individual and collective priority vectors from the self-confident multiplicative preference relations. Then, a two-step feedback adjustment mechanism is used to assist the decision makers to improve the consensus level, which adjusts both the preference values and the self-confidence levels. The simulation experiments are devised to testify the efficiency of the proposed consensus building framework. Simulation results show that compared with only adjusting the preference values in the iteration-based consensus model, adjusting both the preference values and the self-confidence levels can accelerate the consensus success ratio and improve the consensus success ratio.