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Pairwise opposite matrix and its cognitive prioritization operators: comparisons with pairwise reciprocal matrix and analytic prioritization operators

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  • K K F Yuen

    (Zirve University, Gaziantep, Turkey)

Abstract

The pairwise reciprocal matrix (PRM) of the analytic hierarchy/network process has been investigated by many scholars. However, there are significant queries about the appropriateness of using the PRM to represent the pairwise comparison. This research proposes a pairwise opposite matrix (POM) as the ideal alternative with respect to the human linguistic cognition of the rating scale of the paired comparison. Several cognitive prioritization operators (CPOs) are proposed to derive the individual utility vector (or priority vector) of the POM. Not only are the rigorous mathematical proofs of the new models demonstrated, but solutions of the CPOs are also illustrated by the presentation of graph theory. The comprehensive numerical analyses show how the POM performs better than the PRM. POM and CPOs, which correct the fallacy of the PRM associated with its prioritization operators, should be the ideal solutions for multi-criteria decision-making problems in various fields.

Suggested Citation

  • K K F Yuen, 2012. "Pairwise opposite matrix and its cognitive prioritization operators: comparisons with pairwise reciprocal matrix and analytic prioritization operators," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(3), pages 322-338, March.
    • Handle: RePEc:pal:jorsoc:v:63:y:2012:i:3:p:322-338
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    Citations

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    Cited by:

    1. Kevin Kam Fung Yuen, 2014. "The Least Penalty Optimization Prioritization Operators for the Analytic Hierarchy Process: A Revised Case of Medical Decision Problem of Organ Transplantation," Systems Engineering, John Wiley & Sons, vol. 17(4), pages 442-461, December.
    2. Koczkodaj, W.W. & Szybowski, J., 2015. "Pairwise comparisons simplified," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 387-394.
    3. Zhou, Wei & Xu, Zeshui, 2016. "Generalized asymmetric linguistic term set and its application to qualitative decision making involving risk appetites," European Journal of Operational Research, Elsevier, vol. 254(2), pages 610-621.
    4. Chih-Hsuan Wang, 2019. "Association rule mining and cognitive pairwise rating based portfolio analysis for product family design," Journal of Intelligent Manufacturing, Springer, vol. 30(4), pages 1911-1922, April.
    5. Kevin Kam Fung Yuen, 2022. "Decision models for information systems planning using primitive cognitive network process: comparisons with analytic hierarchy process," Operational Research, Springer, vol. 22(3), pages 1759-1785, July.

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