Annals of Operations Research

, Volume 271, Issue 2, pp 1045–1066 | Cite as

A DEMATEL-based completion method for incomplete pairwise comparison matrix in AHP

  • Xinyi Zhou
  • Yong Hu
  • Yong DengEmail author
  • Felix T. S. Chan
  • Alessio Ishizaka
Original Research


Pairwise comparison matrix (PCM) as a crucial component of Analytic Hierarchy Process (AHP) presents the preference relations among alternatives. However, in many cases, the PCM is difficult to be completed, which obstructs the subsequent operations of the classical AHP. In this paper, based on decision-making and trial evaluation laboratory (DEMATEL) method which has ability to derive the total relation matrix from direct relation matrix, a new completion method for incomplete pairwise comparison matrix (iPCM) is proposed. The proposed method provides a new perspective to estimate the missing values in iPCMs with explicit physical meaning, which is straightforward and flexible. Several experiments are implemented as well to present the completion ability of the proposed method and some insights into the proposed method and matrix consistency.


AHP Pairwise comparison matrix Completion method Missing values DEMATEL 



The authors greatly appreciate the reviewer’s constructive suggestions and the editor’s encouragement. The work is partially supported by National Natural Science Foundation of China (Grant Nos. 61573290, 61503237).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Xinyi Zhou
    • 1
    • 2
  • Yong Hu
    • 3
  • Yong Deng
    • 1
    • 3
    • 4
    Email author
  • Felix T. S. Chan
    • 5
  • Alessio Ishizaka
    • 6
  1. 1.Institute of Fundamental and Frontier ScienceUniversity of Electronic Science and Technology of ChinaChengduChina
  2. 2.Department of Electrical Engineering and Computer ScienceSyracuse UniversitySyracuseUSA
  3. 3.Big Data Decision InstituteJinan UniversityTianheChina
  4. 4.School of Computer and Information ScienceSouthwest UniversityChongqingChina
  5. 5.Department of Industrial and Systems EngineeringThe Hong Kong Polytechnic UniversityHung HomHong Kong
  6. 6.Portsmouth Business School, Richmond BuildingUniversity of PortsmouthPortsmouthUK

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