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An intelligent decomposition of pairwise comparison matrices for large-scale decisions

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  • Jalao, Eugene Rex
  • Wu, Teresa
  • Shunk, Dan

Abstract

A Pairwise Comparison Matrix (PCM) has been used to compute for relative priorities of elements and are integral components in widely applied decision making tools: the Analytic Hierarchy Process (AHP) and its generalized form, the Analytic Network Process (ANP). However, PCMs suffer from several issues limiting their applications to large-scale decision problems. These limitations can be attributed to the curse of dimensionality, that is, a large number of pairwise comparisons need to be elicited from a decision maker. This issue results to inconsistent preferences due to the limited cognitive powers of decision makers. To address these limitations, this research proposes a PCM decomposition methodology that reduces the elicited pairwise comparisons. A binary integer program is proposed to intelligently decompose a PCM into several smaller subsets using interdependence scores among elements. Since the subsets are disjoint, the most independent pivot element is identified to connect all subsets to derive the global weights of the elements from the original PCM. As a result, the number of pairwise comparison is reduced and consistency is of the comparisons is improved. The proposed decomposition methodology is applied to both AHP and ANP to demonstrate its advantages.

Suggested Citation

  • Jalao, Eugene Rex & Wu, Teresa & Shunk, Dan, 2014. "An intelligent decomposition of pairwise comparison matrices for large-scale decisions," European Journal of Operational Research, Elsevier, vol. 238(1), pages 270-280.
    • Handle: RePEc:eee:ejores:v:238:y:2014:i:1:p:270-280
    DOI: 10.1016/j.ejor.2014.03.032
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    References listed on IDEAS

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    1. Dimitris K. Despotis & Dimitris Derpanis, 2008. "A Min–Max Goal Programming Approach To Priority Derivation In Ahp With Interval Judgements," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 175-182.
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    4. 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.
    5. Saaty, Thomas L., 1990. "How to make a decision: The analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 48(1), pages 9-26, September.
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    Cited by:

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    2. Chao, Xiangrui & Kou, Gang & Li, Tie & Peng, Yi, 2018. "Jie Ke versus AlphaGo: A ranking approach using decision making method for large-scale data with incomplete information," European Journal of Operational Research, Elsevier, vol. 265(1), pages 239-247.
    3. Kheybari, Siamak & Rezaie, Fariba Mahdi & Farazmand, Hadis, 2020. "Analytic network process: An overview of applications," Applied Mathematics and Computation, Elsevier, vol. 367(C).
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    6. Mamata Sahu & Anjana Gupta & Aparna Mehra, 2017. "Hierarchical clustering of interval-valued intuitionistic fuzzy relations and its application to elicit criteria weights in MCDM problems," OPSEARCH, Springer;Operational Research Society of India, vol. 54(2), pages 388-416, June.

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