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On Mathematical Structures On Pairwise Comparisons Matrices With Coefficients In A Group Arising From Quantum Gravity

Author

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  • Jean-Pierre Magnot

    (LAREMA - Laboratoire Angevin de Recherche en Mathématiques - UA - Université d'Angers - CNRS - Centre National de la Recherche Scientifique)

Abstract

We describe the mathematical properties of pairwise comparisons matrices with coefficients in an arbitrary group. We provide a vocabulary adapted for the description of main algebraic properties of inconsistency maps, describe an example where the use of a non abelian group is necessary. Algebraic , topological, geometric and probabilistic aspects are considered.

Suggested Citation

  • Jean-Pierre Magnot, 2019. "On Mathematical Structures On Pairwise Comparisons Matrices With Coefficients In A Group Arising From Quantum Gravity," Post-Print hal-01835958, HAL.
    • Handle: RePEc:hal:journl:hal-01835958
    DOI: 10.1016/j.heliyon.2019.e01821
    Note: View the original document on HAL open archive server: https://hal.science/hal-01835958
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    References listed on IDEAS

    as
    1. Matteo Brunelli & Michele Fedrizzi, 2015. "Axiomatic properties of inconsistency indices for pairwise comparisons," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(1), pages 1-15, January.
    2. Jean-Pierre Magnot, 2018. "A Mathematical Bridge between Discretized Gauge Theories in Quantum Physics and Approximate Reasoning in Pairwise Comparisons," Post-Print hal-01831631, HAL.
    3. Simone Farinelli, 2009. "Geometric Arbitrage Theory and Market Dynamics Reloaded," Papers 0910.1671, arXiv.org, revised Jul 2021.
    4. Biswa Sengupta & Arturo Tozzi & Gerald K Cooray & Pamela K Douglas & Karl J Friston, 2016. "Towards a Neuronal Gauge Theory," PLOS Biology, Public Library of Science, vol. 14(3), pages 1-12, March.
    5. Jean-Pierre Magnot, 2018. "The group of diffeomorphisms of a non-compact manifold is not regular," Post-Print hal-01831632, HAL.
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    Cited by:

    1. Jean-Pierre Magnot & Jiří Mazurek & Viera Cernanova, 2021. "A gradient method for inconsistency reduction of pairwise comparisons matrices," Working Papers hal-03313878, HAL.
    2. Jean-Pierre Magnot, 2020. "Inconsistency in pairwise comparisons as an Abelian Yang-Mills theory," Working Papers hal-03091527, HAL.

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