Group Decision and Negotiation

, Volume 28, Issue 6, pp 1167–1191 | Cite as

Direct Iterative Procedures for Consensus Building with Additive Preference Relations Based on the Discrete Assessment Scale

  • Zhibin WuEmail author
  • Jie Xiao
  • Ivan Palomares


Individual consistency and group consensus are both important when seeking reliable and satisfying solutions for group decision making (GDM) problems using additive preference relations (APRs). In this paper, two new algorithms are proposed to facilitate the consensus reaching process, the first of which is used to improve the individual consistency level, and the second of which is designed to assist the group to achieve a predefined consensus level. Unlike previous GDM studies for consistency and consensus building, the proposed algorithms are essentially heuristic, modify only some of the elements in APRs to reduce the number of preference modifications in the consistency and consensus process, and have modified preferences that belong to the original evaluation scale to make the generated suggestions easier to understand. In particular, the consensus algorithm ensures that the individual consistency level is still acceptable when the predefined consensus level is achieved. Finally, classical examples and simulations are given to demonstrate the effectiveness of the proposed approaches.


Group decision making Additive preference relation Consistency Consensus 



This work was supported by National Natural Science Foundation of China under Grant 71671118.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Uncertainty Decision-Making Laboratory, Business SchoolSichuan UniversityChengduPeople’s Republic of China
  2. 2.School of Computer Science, Electrical and Electronic Engineering, and Engineering MathematicsUniversity of BristolBristolUK

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