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New State of MCDM in the 21st Century pp 47–56Cite as

A New Consistency Index for Comparison Matrices in the ANP

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 648))

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.

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Acknowledgements

This research has been supported by grants from the National Natural Science Foundation of China (#70901011, #70901015, and # 70921061).

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Authors and Affiliations

  1. School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, 610054, China

    Daji Ergu, Gang Kou & Yi Peng

  2. Southwest University for Nationalities, Chengdu, 610200, China

    Daji Ergu

  3. College of Information Science & Technology, University of Nebraska at Omaha, Omaha, NE, 68182, USA

    Yong Shi

  4. Research Center on Fictitious Economy and Data Sciences, Chinese Academy of Sciences, Beijing, 100190, China

    Yong Shi

Authors
  1. Daji Ergu
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  2. Gang Kou
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  3. Yi Peng
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  4. Yong Shi
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Corresponding author

Correspondence to Yi Peng .

Editor information

Editors and Affiliations

  1. Research Cntr on Fict. Econ. & Data Sci., Chinese Academy of Sciences, Zhongguancun East Road, No 80 Building 6, Room 203, Beijing, 10090, China, People's Republic

    Yong Shi

  2. College of Information Science and Technology, University of Nebraska at Omaha, Omaha, NE 68182, USA

    Yong Shi

  3. Academy of Mathematics and, Chinese Academy of Sciences, Zhonguancun East Road 55Haidian, Beijing, NE, 100190, China, People's Republic

    Shouyang Wang

  4. School of Management and Economics, University of Electr. Science & Technol., Zhonguancun East Road No. 55, Haidian, Chengdu, 610054, China, People's Republic

    Gang Kou PhD

  5. Aalto University School of Economics, 21210, 00076, Aalto, Finland

    Jyrki Wallenius

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© 2011 Springer-Verlag Berlin Heidelberg

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Ergu, D., Kou, G., Peng, Y., Shi, Y. (2011). A New Consistency Index for Comparison Matrices in the ANP. In: Shi, Y., Wang, S., Kou, G., Wallenius, J. (eds) New State of MCDM in the 21st Century. Lecture Notes in Economics and Mathematical Systems, vol 648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19695-9_4

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