Soft Computing

, Volume 23, Issue 24, pp 13691–13707 | Cite as

Deriving priority weights from hesitant fuzzy preference relations in view of additive consistency and consensus

  • Jian Li
  • Zhong-Xing WangEmail author
Methodologies and Application


Given that deriving priority weights is essential in group decision making, this study focuses on deriving priority weights from hesitant fuzzy preference relation (HFPR) in view of additive consistency and consensus. To achieve this goal, first, a new additive consistency concept of the HFPR is proposed. The main feature of the proposed additive consistency concept is that it considers all evaluation information provided by decision makers, that is, neither add values into nor remove values from hesitant fuzzy elements. Second, a programming model is constructed to verify the complete additive consistency of HFPR, an additive consistency index is suggested to validate its consistency degree, and then, a programming model is established to improve its consistency degree. Third, an algorithm is designed to derive a priority weight vector from the HFPR, and the proposed algorithm not only addresses the situation in which the HFPR is a complete and acceptable additive consistency. Fourth, a programming model is presented to determine the decision makers’ weights, and then, a consensus measure index based on extraction priority weight vectors is introduced. Moreover, a programming model is constructed to derive the priority weights that correspond to expected consensus levels. Finally, the most cost-effective car selection problems are provided to illustrate the effectiveness of the proposed method. Comparative studies with several existing methods are also provided.


Group decision making Consensus Hesitant fuzzy preference relation Additive consistency Priority weights 



The authors thank the anonymous reviewers and the editor for their insightful and constructive comments and suggestions that have led to an improved version of this paper. This work was supported by the Key Research and Development Program of Guangxi (Nos. 2017AB16004), Promotion project of Middle-aged and Young Teachers’ Basic Scientific Research Ability in Universities of Guangxi (No. 2019KY0963) and the Research Funds for the Guangxi University Xingjian College of Science and Liberal Arts (Nos. Y2018ZKT01).

Compliance with ethical standards

Conflict of interest

All authors have declared that they have no conflicts of interest.

Informed consent

Informed consent was unnecessary because no human or animals were involved.

Human and animal rights

This article does not contain any studies with human or animal subjects performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of XingJian College of Science and Liberal ArtsGuangxi UniversityNanningPeople’s Republic of China
  2. 2.School of Mathematics and Information ScienceGuangxi UniversityNanningPeople’s Republic of China

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