A Minimum Cost Consensus Model Considering Individual Tolerance Levels

Abstract

The consensus process plays a decisive role in a group decision making problem. From a perspective of optimization, various consensus models have been presented to help the group reach a predefined consensus level. The aim of this paper is to propose a new minimum cost consensus model and its dual model in an uncertain situation. In this new model, different individual tolerance levels are allowed and the group opinion is obtained by the weighted average (WA) operator. In such a model, the moderator does not need to pay if the changed opinion of a decision maker is still under the tolerance level of that decision maker. Moreover, the decision makers do not need to change their opinions into a common value to reach the consensus level. The proposed dual consensus model has some significant economic interpretations. Some properties with respect to the two proposed consensus models are analyzed. The validity of the proposed models is illustrated by a numerical example.