A two-stage consensus reaching model for group decision making with reciprocal fuzzy preference relations

  • Yejun XuEmail author
  • Nannan Wu
Methodologies and Application


Reciprocal fuzzy preference relation (FPR) is a hot topic in the research field of group decision making (GDM). Within the framework of GDM, a two-stage consensus reaching model is proposed to modify the decision makers’ (DMs’) FPRs. In the first stage which is called consistency improving stage, a consistency index and an iterative algorithm are employed to measure and improve individual consistency, respectively. In each iteration of the algorithm, only one pair of preference values, which deviates the most from the corresponding elements in the consistent FPR matrix, are modified to keep the DM’s original information as much as possible. In the second stage which is called consensus reaching stage, individual consensus index and group consensus index are applied to measure consensus. A convex quadratic programming model is developed to help DMs reach consensus. Some desired properties of the model are also investigated and testified. What’s more, the final individual consistency is also limited to an acceptable threshold. Finally, a practical example is used to illustrate the validity of the proposed consensus model.


GDM Reciprocal fuzzy preference relation Individual consistency Consensus model 



The authors are very grateful to associate editor and the anonymous reviewers for their constructive comments and suggestions that have helped to improve the quality of this paper. This work was partly supported by the National Natural Science Foundation of China (NSFC) under Grants (No. 71471056), Qing Lan Project of Jiangsu Province.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Business SchoolHohai UniversityNanjingPeople’s Republic of China

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