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Inconsistency of the judgment matrix in the AHP method and the decision maker’s knowledge

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  • Szczypińska, Anna
  • Piotrowski, Edward W.

Abstract

In this paper, we propose a method for a quantitative estimation of the decision maker’s knowledge in the context of the Analytic Hierarchy Process (AHP) in cases where the judgment matrix is inconsistent. We show that the matrix of deviation from the transitivity condition corresponds to the rate matrix for transaction costs in the financial market. For the quantitative estimation of the decision maker’s professionalism, we apply the Ising model and thermodynamics tools.

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  • 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.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:6:p:907-915
    DOI: 10.1016/j.physa.2008.11.034
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    1. Piotrowski, Edward W & Sładkowski, Jan, 2004. "Arbitrage risk induced by transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(1), pages 233-239.
    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.
    3. 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.
    4. Vargas, Luis G., 1990. "An overview of the analytic hierarchy process and its applications," European Journal of Operational Research, Elsevier, vol. 48(1), pages 2-8, September.
    5. Edward W. Piotrowski & Jan Sladkowski, "undated". "The Thermodynamics of Portfolios," Departmental Working Papers 2, University of Bialtystok, Department of Theoretical Physics.
    6. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
    7. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
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