Consensus building for interval MAGDM problems based on integer programming models

This paper is primarily interested in optimization consensus models in the context of multiple attribute group decision making (MAGDM) where the uncertain information can be represented by interval numbers. The preservation of the original opinion scales in the modified preferences, and the scarce number of consensus approaches for the interval MAGDM problem are the major motivations to develop new optimal consensus models. Two general consensus rules from a cost perspective are used as the objectives: one is to minimize the amount of preference changes and the other is to minimize the number of modifications. Based on the two rules, two consensus models based on the Manhattan distance are presented. The presented models can be solved by integer linear programming techniques. The main advantage of the proposed consensus models comparing to the existing approaches is that the generated preferences are belonged to the original scales. These models can be extended to other uncertain situations and can find wild applications in decision science.