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Computationally efficient orthogonalization for pairwise comparisons method

Author

Listed:
  • Benítez, Julio
  • Koczkodaj, Waldemar W.
  • Kowalczyk, Adam

Abstract

Orthogonalization is one of few mathematical methods conforming to mathematical standards for approximation. Finding a consistent PC matrix of a given an inconsistent PC matrix is the main goal of a pairwise comparisons method. We introduce an orthogonalization for pairwise comparisons matrix based on a generalized Frobenius inner matrix product. The proposed theory is supported by numerous examples and visualizations.

Suggested Citation

  • Benítez, Julio & Koczkodaj, Waldemar W. & Kowalczyk, Adam, 2024. "Computationally efficient orthogonalization for pairwise comparisons method," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    • Handle: RePEc:eee:apmaco:v:473:y:2024:i:c:s0096300324001231
    DOI: 10.1016/j.amc.2024.128651
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    References listed on IDEAS

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    1. Julio Benítez & Silvia Carpitella & Joaquín Izquierdo, 2023. "Efficient sampling of pairwise comparisons in decision-making," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 74(8), pages 1860-1877, August.
    2. Josep Colomer, 2013. "Ramon Llull: from ‘Ars electionis’ to social choice theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 317-328, February.
    3. Koczkodaj, W.W. & Szybowski, J., 2015. "Pairwise comparisons simplified," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 387-394.
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