Soft Computing

, Volume 22, Issue 6, pp 1933–1943 | Cite as

Analyzing Saaty’s consistency test in pairwise comparison method: a perspective based on linguistic and numerical scale

  • Hengjie Zhang
  • Xin Chen
  • Yucheng Dong
  • Weijun Xu
  • Shihua Wang
Methodologies and Application


The consistency test is a vital basis of the pairwise comparison method, which is performed to ensure that the decision maker is being logical in his/her pairwise comparisons. In the analytic hierarchy process, the pairwise comparison method with a fixed numerical scale has been employed. In this study, we provide a systematic review analysis regarding the inconsistency causes in the pairwise comparison method with a fixed numerical scale, and propose the paradoxes on Saaty’s consistency test in this pairwise comparison method. Meanwhile, based on the use of the consistency-driven linguistic methodology, we propose a novel approach from a perspective of the linguistic and numerical scale to deal with the inconsistency in the pairwise comparison method.


Multiple attribute decision making Pairwise comparison matrix Consistency Numerical scale The 2-tuple linguistic representation model Consistency-driven linguistic methodology 



This work was supported by the grants (Nos. 71571124, 71171160, 71471065) from NSF of China, the grant (No. skqy201606) from Sichuan University, the grant (No. 2015GD05) from South China University of Technology, the grant (No. GDUPTLAB201602) from the Open Fund of Guangdong Provincial Key Laboratory of Petrochemical Equipment Fault Diagnosis and the grant (No. 2015B090903084) from Guangdong Provincial Science and Technology Cooperation Project.

Compliance with ethical standards

Conflict of interest

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

Human and animal studies

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


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Hengjie Zhang
    • 1
  • Xin Chen
    • 2
  • Yucheng Dong
    • 1
  • Weijun Xu
    • 3
  • Shihua Wang
    • 4
  1. 1.Business SchoolSichuan UniversityChengduPeople’s Republic of China
  2. 2.School of ScienceBeijing Forestry UniversityBeijingPeople’s Republic of China
  3. 3.School of Business AdministrationSouth China University of TechnologyGuangzhouPeople’s Republic of China
  4. 4.Guangdong Provincial Key Laboratory of Petrochemical Equipment Fault DiagnosisGuangdong University of Petrochemical TechnologyMaomingPeople’s Republic of China

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