Optimal improvement of the best and worst consistency levels for interval additive preference relations

Abstract The best consistency index (BCI) and the worst consistency index (WCI) were introduced into interval additive preference relations (IAPRs) to guarantee that any APR within an IAPR would have a satisfactory best or worst consistency. However, the methods for controlling the BCI and WCI consistencies were not clear, and consensus reaching problems based on the BCI and WCI, which are a key issue in group decision making using IAPRs, have not yet been addressed. Therefore, to address this particular omission, this paper suggests various optimization approaches for the modeling of both consistency and consensus. First, an APR that corresponds to the worst consistency is determined using the IAPR boundary elements, after which an optimization model is introduced to improve the BCI and WCI that minimizes the amount of change. It was found that if all individual IAPRs had acceptable WCIs, the group IAPR also had an acceptable WCI for the group decision making. An optimal consensus model is also proposed to deal with the consistency and consensus. These models were found to be able to effectively manage the worst consistency in the decision process. Some numerical examples and comparison analyses are given to validate the efficiency of the developed decision models.