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Projective Market Model Approach to AHP Decision-Making

Listed author(s):
  • Anna Szczypinska


  • Edward W. Piotrowski


In this paper we describe market in projective geometry language and give 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 projective geometry formalism and generalise it to intransitive case. We give financial interpretations of such 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 such extended model.

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Paper provided by University of Bialtystok, Department of Theoretical Physics in its series Departmental Working Papers with number 32.

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Date of creation:
Handle: RePEc:sla:eakjkl:32
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  1. Piotrowski, E.W & SÅ‚adkowski, J, 2002. "Quantum market games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 208-216.
  2. 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.
  3. Zambrzycka, Anna & Piotrowski, Edward W., 2007. "The matrix rate of return," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 347-353.
  4. Anna Zambrzycka & Edward W. Piotrowski, "undated". "The Matrix Rate of Return," Departmental Working Papers 25, University of Bialtystok, Department of Theoretical Physics.
  5. 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.
  6. Kwiesielewicz, M., 1996. "The logarithmic least squares and the generalized pseudoinverse in estimating ratios," European Journal of Operational Research, Elsevier, vol. 93(3), pages 611-619, September.
  7. Edward W. Piotrowski & Jan Sladkowski, "undated". "Geometry of Financial Markets - Towards Information Theory Model of Markets," Departmental Working Papers 26, University of Bialtystok, Department of Theoretical Physics.
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