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Further Discussions on Induced Bias Matrix Model for the Pair-Wise Comparison Matrix

Author

Listed:
  • Daji Ergu

    (University of Electronic Science and Technology of China
    Southwest University for Nationalities)

  • Gang Kou

    (University of Electronic Science and Technology of China)

  • János Fülöp

    (Hungarian Academy of Sciences)

  • Yong Shi

    (University of Nebraska at Omaha
    Chinese Academy of Sciences)

Abstract

The inconsistency issue of pairwise comparison matrices has been an important subject in the study of the analytical network process. Most inconsistent elements can efficiently be identified by inducing a bias matrix only based on the original matrix. This paper further discusses the induced bias matrix and integrates all related theorems and corollaries into the induced bias matrix model. The theorem of inconsistency identification is proved mathematically using the maximum eigenvalue method and the contradiction method. In addition, a fast inconsistency identification method for one pair of inconsistent elements is proposed and proved mathematically. Two examples are used to illustrate the proposed fast identification method. The results show that the proposed new method is easier and faster than the existing method for the special case with only one pair of inconsistent elements in the original comparison matrix.

Suggested Citation

  • Daji Ergu & Gang Kou & János Fülöp & Yong Shi, 2014. "Further Discussions on Induced Bias Matrix Model for the Pair-Wise Comparison Matrix," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 980-993, June.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:3:d:10.1007_s10957-012-0223-2
    DOI: 10.1007/s10957-012-0223-2
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    References listed on IDEAS

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