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Improved Consistency Ratio for Pairwise Comparison Matrix in Analytic Hierarchy Processes

Author

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  • L. N. Pradeep Kumar Rallabandi

    (JNT University Kakinada, Kakinada 533003, Andhra Pradesh, India)

  • Ravindranath Vandrangi

    (JNT University Kakinada, Kakinada 533003, Andhra Pradesh, India)

  • Subba Rao Rachakonda

    (Sri Vishnu Engineering College for Women, Bhimavaram 534202, Andhra Pradesh, India)

Abstract

The analytical hierarchy process (AHP) uses pairwise comparison matrix (PCM) to rank a known set of alternatives. Sometimes the comparisons made by the experts may be inconsistent which results in incorrect weights and rankings for the AHP. In this paper, a method is proposed which identifies inconsistent elements in a PCM and revises them iteratively until the inconsistency is reduced to an acceptable level. An error function similar to chi-square is used to identify the inconsistent elements which are revised with suitable values. The method is illustrated with some numerical examples mentioned in the literature and a comparative study of the results in terms of deviation from the PCM and preservation of original information is taken up. Monte Carlo simulation experiments over a large set of random matrices indicate that the proposed method converges for the moderately inconsistent matrices.

Suggested Citation

  • L. N. Pradeep Kumar Rallabandi & Ravindranath Vandrangi & Subba Rao Rachakonda, 2016. "Improved Consistency Ratio for Pairwise Comparison Matrix in Analytic Hierarchy Processes," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-19, June.
    • Handle: RePEc:wsi:apjorx:v:33:y:2016:i:03:n:s0217595916500202
    DOI: 10.1142/S0217595916500202
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    References listed on IDEAS

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    1. Saaty, Thomas L., 2003. "Decision-making with the AHP: Why is the principal eigenvector necessary," European Journal of Operational Research, Elsevier, vol. 145(1), pages 85-91, February.
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    3. Ergu, Daji & Kou, Gang & Peng, Yi & Shi, Yong, 2011. "A simple method to improve the consistency ratio of the pair-wise comparison matrix in ANP," European Journal of Operational Research, Elsevier, vol. 213(1), pages 246-259, August.
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    7. Patrick T. Harker & Luis G. Vargas, 1987. "The Theory of Ratio Scale Estimation: Saaty's Analytic Hierarchy Process," Management Science, INFORMS, vol. 33(11), pages 1383-1403, November.
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