Soft Computing

, Volume 23, Issue 2, pp 583–597 | Cite as

Exploiting the priority weights from interval linguistic fuzzy preference relations

  • Fanyong Meng
  • Jie Tang
  • Zeshui XuEmail author
Methodologies and Application


Interval linguistic fuzzy preference relations (ILFPRs) are powerful tools to denote the decision makers’ uncertain qualitative preferences. To avoid the inconsistent ranking results, consistency analysis is very critical. This paper introduces a new additive consistency concept for ILFPRs, which satisfies all properties of the additive consistency concept for fuzzy preference relations. Then, a model to judging the additive consistency of ILFPRs is constructed. When ILFPRs are inconsistent, an approach to deriving additive consistent ILFPRs is presented. Considering the incomplete case, goal programming models to determining the missing values are established. Subsequently, a distance measure-based group consensus index is given to measuring the consensus of individual ILFPRs. Furthermore, a new method for group decision making with ILFPRs is developed, which is based on the additive consistency and consensus analysis. Finally, two numerical examples are offered to show the application of the developed procedure, and a comparison analysis is performed.


Group decision making Interval linguistic fuzzy preference relation Additive consistency Consensus Programming model 



This work was supported by the National Natural Science Foundation of China (Nos. 71571192, 71571123, 71671188, and 71501189), the National Social Science Foundation of China (No. 16BJY119), the Innovation-Driven Planning Foundation of Central South University (No. 2016CXS027), the State Key Program of National Natural Science of China (No. 71431006), the Projects of Major International Cooperation NSFC (No. 71210003), the Hunan Province Foundation for Distinguished Young Scholars of China (No. 2016JJ1024), and the China Postdoctoral Science Foundation (No. 2016M602170).

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

Ethical approval

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


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of International AuditNanjing Audit UniversityNanjingChina
  2. 2.Business SchoolSichuan UniversityChengduChina
  3. 3.School of BusinessCentral South UniversityChangshaChina
  4. 4.School of Computer and SoftwareNanjing University of Information Science and TechnologyNanjingChina

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