A consensus model for group decision making with self‐confident linguistic preference relations

Preference relation has been one of the most useful tools for experts to express their comparison information over alternatives in group decision-making (GDM) problems. Recently, a new type of preference relations called linguistic preference relations with self-confidence (LPRs-SC) has been proposed, which makes multiple self-confidence levels into consideration when experts provide their preferences. This study focuses on the consensus reaching process for GDM with LPRs-SC. To do that, some new operational laws for LPRs-SC are presented. Subsequently, an iteration-based consensus proposal for LPRs-SC is proposed. In the proposal, we aggregate the individual LPRs-SC using a self-confidence indices-based method which gives more importance to the most self-confident experts. A self-confidence score function is presented to derive the individual and collective priority vectors. Moreover, considering experts’ acceptable adjustment range of preference values, a two-step feedback adjustment mechanism is utilized to improve the consensus level, which adjusts both the preference values and the self-confidence levels. Finally, an example and some analyses are furnished to demonstrate the feasibility and effectiveness of the proposed method.