Optimal consensus models for group decision making under linguistic preference relations

This paper proposes an optimal consensus model to derive weights for linguistic preference relations (LPRs). Two indexes, an individual‐to‐group consensus index (ICI) and a collective consensus index (CCI), are introduced. An iterative algorithm is presented to describe the consensus reaching process. By changing the weights and modifying a pair of individuals' comparison judgments–which have largest deviation value to the group judgments–the consensus reaching process can terminate, while both ICI and CCI are controlled with predefined thresholds. The algorithm aims to preserve the decision makers’ original information as much as possible. The model and algorithm are then extended to handle the uncertain additive LPRs. Finally, two examples are given to show the effectiveness of the proposed methods.