Optimal consistency and consensus models for interval additive preference relations: A discrete distribution perspective

To assist in the consensus reaching process, this article presents optimization models with interval additive preference relations (APRs) drawn from pairwise comparisons. First, consistency models are proposed to obtain additively consistent interval APRs for continuous and discrete scale cases, after which consensus models are established to arrive at a predefined consensus level for the two cases. These models seek to minimize the amount of preference changes and can be solved using linear or integer linear programming techniques. While the obtained solutions may not be unique, a second stage model is introduced to reduce the uncertainty degrees in the suggested preferences. Compared to existing approaches, the proposed models have two major advantages: the derived solution can be limited to the easy to understand original scales, and refined solutions can be determined using multi-stage optimization. Finally, several numerical examples are given to verify the proposed models, and several simulations are conducted to demonstrate the potential behaviour of the presented models in practical applications.