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Projective market model approach to AHP decision making

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  • Szczypińska, Anna
  • Piotrowski, Edward W.

Abstract

In this paper, we describe market in the projective geometry language and give the definition of a matrix of market rate, which is related to the matrix rate of return and the matrix of judgements in the Analytic Hierarchy Process (AHP). We use these observations to extend the AHP model to the projective geometry formalism and generalise it to an intransitive case. We give financial interpretations of such a generalised model and propose its simplification. The unification of the AHP model and projective aspect of portfolio theory suggests a wide spectrum of new applications for such an extended model.

Suggested Citation

  • Szczypińska, Anna & Piotrowski, Edward W., 2008. "Projective market model approach to AHP decision making," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3982-3986.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:15:p:3982-3986
    DOI: 10.1016/j.physa.2008.01.053
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    References listed on IDEAS

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    1. Marcin Makowski & Edward W. Piotrowski, "undated". "Quantum Cat's Dilemma: an Example of Intransitivity in a Quantum Game," Departmental Working Papers 28, University of Bialtystok, Department of Theoretical Physics.
    2. Piotrowski, Edward W. & Sładkowski, Jan, 2007. "Geometry of financial markets—Towards information theory model of markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 228-234.
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    9. Ernest H. Forman & Saul I. Gass, 2001. "The Analytic Hierarchy Process---An Exposition," Operations Research, INFORMS, vol. 49(4), pages 469-486, August.
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    1. Wang, Jiang-Jiang & Jing, You-Yin & Zhang, Chun-Fa & Shi, Guo-Hua & Zhang, Xu-Tao, 2008. "A fuzzy multi-criteria decision-making model for trigeneration system," Energy Policy, Elsevier, vol. 36(10), pages 3823-3832, October.
    2. Szczypińska, Anna & Piotrowski, Edward W., 2009. "Inconsistency of the judgment matrix in the AHP method and the decision maker’s knowledge," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 907-915.
    3. Waldhausen, Henry & Griffin, Christopher, 2025. "Binary option market manipulation by influencing belief dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 680(C).
    4. Jing, You-Yin & Bai, He & Wang, Jiang-Jiang, 2012. "A fuzzy multi-criteria decision-making model for CCHP systems driven by different energy sources," Energy Policy, Elsevier, vol. 42(C), pages 286-296.
    5. Edward W. Piotrowski & Jerzy Luczka, "undated". "The relativistic velocity addition law optimizes a forecast gambler's profit," Departmental Working Papers 31, University of Bialtystok, Department of Theoretical Physics.

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