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A New Consistency Index for Comparison Matrices in the ANP

In: New State of MCDM in the 21st Century

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)

  • Yi Peng

    (University of Electronic Science and Technology of China)

  • Yong Shi

    (University of Nebraska at Omaha
    Chinese Academy of Sciences)

Abstract

The inconsistency test is more difficult in the analytical network process (ANP) than in the analytical hierarchy process (AHP) because there are more comparison matrices in the ANP. The consistency ratio (CR) introduced by Saaty for the AHP is used for inconsistency test in the ANP. When the number of comparison matrices increases, the inconsistency test of comparison matrices in the ANP becomes complicated. In an attempt to simplify the inconsistency test, this paper proposes a maximum eigenvalue threshold as the consistency index for ANP, which is mathematically equivalent to the CR method. In addition, a block diagonal matrix is introduced for the comparison matrices in the ANP to conduct inconsistency tests simultaneously for all comparison matrices. An illustrative example is used to show the effectiveness and the simplicity of the proposed maximum eigenvalue threshold method.

Suggested Citation

  • Daji Ergu & Gang Kou & Yi Peng & Yong Shi, 2011. "A New Consistency Index for Comparison Matrices in the ANP," Lecture Notes in Economics and Mathematical Systems, in: Yong Shi & Shouyang Wang & Gang Kou & Jyrki Wallenius (ed.), New State of MCDM in the 21st Century, chapter 0, pages 47-56, Springer.
    • Handle: RePEc:spr:lnechp:978-3-642-19695-9_4
    DOI: 10.1007/978-3-642-19695-9_4
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    Cited by:

    1. Daji Ergu & Gang Kou & Jennifer Shang, 2014. "A Modular-Based Supplier Evaluation Framework: A Comprehensive Data Analysis of ANP Structure," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 13(05), pages 883-916.

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