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Using genetic algorithm to improve consistency and retain authenticity in the analytic hierarchy process

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  • Amarnath Bose

    (Birla Institute of Management Technology)

Abstract

The quality of decision using the analytic hierarchy process (AHP) depends upon the consistency of the pairwise comparison matrices (PCM) in the AHP hierarchy. While several studies describe methods to improve consistency, the related issue of retaining authenticity of the judgements has received far less attention. In this paper, a multi-objective genetic algorithm is presented for the purpose of reducing the inconsistency of a PCM while ensuring a high degree of authenticity with respect to the original input. A number of Pareto-optimal solutions are generated as a result of the optimization. Heuristics for choosing one of these PCMs based on a trade-off between consistency and authenticity is also presented. To demonstrate the effectiveness of the proposed method two inconsistent PCMs are selected for rectification. Rectified PCMs from the proposed method as well as from other established methods are compared. It is seen that the proposed method results in consistency that compares favorably with existing methods while retaining a greater degree of authenticity. Though the proposed method is slow and computationally intensive, we believe that this is a cost worth incurring in the interest of reliability and authenticity of judgements.

Suggested Citation

  • Amarnath Bose, 2020. "Using genetic algorithm to improve consistency and retain authenticity in the analytic hierarchy process," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1070-1092, December.
    • Handle: RePEc:spr:opsear:v:57:y:2020:i:4:d:10.1007_s12597-020-00450-z
    DOI: 10.1007/s12597-020-00450-z
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    References listed on IDEAS

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    1. Zeshui, Xu & Cuiping, Wei, 1999. "A consistency improving method in the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 116(2), pages 443-449, July.
    2. Maghsoud Solimanpur & Gholamreza Mansourfar & Farzad Ghayour, 2015. "Optimum portfolio selection using a hybrid genetic algorithm and analytic hierarchy process," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 32(3), pages 379-394, August.
    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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    5. Vaidya, Omkarprasad S. & Kumar, Sushil, 2006. "Analytic hierarchy process: An overview of applications," European Journal of Operational Research, Elsevier, vol. 169(1), pages 1-29, February.
    6. Kuenz Murphy, Catherine, 1993. "Limits on the analytic hierarchy process from its consistency index," European Journal of Operational Research, Elsevier, vol. 65(1), pages 138-139, February.
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    Cited by:

    1. Vijay Pereira & Umesh Bamel, 2023. "Charting the managerial and theoretical evolutionary path of AHP using thematic and systematic review: a decadal (2012–2021) study," Annals of Operations Research, Springer, vol. 326(2), pages 635-651, July.
    2. Sangeeta Pant & Anuj Kumar & Mangey Ram & Yury Klochkov & Hitesh Kumar Sharma, 2022. "Consistency Indices in Analytic Hierarchy Process: A Review," Mathematics, MDPI, vol. 10(8), pages 1-15, April.

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