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El pesar en el proceso analítico jerárquico1

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  • MORENO JIMÉNEZ, J.Mª

    (Departamento Métodos Estadísticos. Universidad de Zaragoza)

  • ESCOBAR URMENETA, Mª T.

    (Departamento Métodos Estadísticos. Universidad de Zaragoza)

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    Abstract

    El trabajo analiza el significado del pesar asociado a las prioridades obtenidas en el Proceso Analítico Jerárquico (AHP), y, tal y como solicitan Loomes y Sudgen (1982) para la Toma de Decisiones (TD) en general, ofrece una expresión de las prioridades de AHP en función del pesar. Se ha encontrado la relación entre el pesar, evaluado tanto en términos absolutos como en términos relativos, y las prioridades obtenidas en AHP para dos procedimientos de normalización (modo distributivo e ideal) y dos de síntesis (aditiva y multiplicativa). Se ha probado que esta relación es independiente del método de normalización, y la forma que adopta depende del método de síntesis y de la forma en que se evalúa el pesar. Si la evaluación del pesar se efectúa en términos absolutos y se emplea la síntesis aditiva se obtienen una relación aditiva; y si el pesar se evalúa en términos relativos y se utiliza la síntesis multiplicativa la relación es multiplicativa. En ambos casos la aplicación de AHP y la minimización del pesar proporcionan los mismos resultados en selección multicriterio de alternativas. The paper analyses the meaning of the regret associated with the priorities obtained with the Analytic Hierarchy Process (AHP), and, as it is required by Loomes and Sudgen (1982) for Decision Making, offers an expression of the AHP priorities in terms of the regret. We have found the relationship between the regret, evaluated both in absolute and in relative terms, and the AHP priorities obtained with two normalization methods (distributive and ideal) and two synthesis procedures (additive and multiplicative). We have proved that this relationship is independent of the normalization method employed, and that the form it adopts depends on the synthesis method and the way the regret is evaluated. If the regret is evaluated in absolute terms and the additive synthesis method is employed, the relationship has an additive form. If the regret is evaluated in relative terms and the multiplicative synthesis method is employed, the relationship is multiplicative. In both cases the application of AHP and the minimizat on of the regret provides the same results in multicriteria selection of alternatives.

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    Bibliographic Info

    Article provided by Estudios de Economía Aplicada in its journal Estudios de Economía Aplicada.

    Volume (Year): 14 (2000)
    Issue (Month): (Abril)
    Pages: 95-115

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    Handle: RePEc:lrk:eeaart:14_1_5

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    Related research

    Keywords: Multicriteria Decision Making; Analytic Hierarchy Process (AHP); Priorities; Regret.;

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    References

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    1. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
    2. Loomes, Graham & Sugden, Robert, 1987. "Testing for Regret and Disappointment in Choice under Uncertainty," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 97(388a), pages 118-29, Supplemen.
    3. Mark J Machina, 1982. ""Expected Utility" Analysis without the Independence Axiom," Levine's Working Paper Archive 7650, David K. Levine.
    4. Quiggin, John, 1990. "Stochastic Dominance in Regret Theory," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 57(3), pages 503-11, July.
    5. Fishburn, Peter C., 1983. "Transitive measurable utility," Journal of Economic Theory, Elsevier, Elsevier, vol. 31(2), pages 293-317, December.
    6. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, Econometric Society, vol. 66(3), pages 497-528, May.
    7. Loomes, Graham & Sugden, Robert, 1986. "Disappointment and Dynamic Consistency in Choice under Uncertainty," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 53(2), pages 271-82, April.
    8. Schoner, Bertram & Wedley, William C. & Choo, Eng Ung, 1993. "A unified approach to AHP with linking pins," European Journal of Operational Research, Elsevier, Elsevier, vol. 64(3), pages 384-392, February.
    9. Loomes, Graham & Sugden, Robert, 1983. "Regret theory and measurable utility," Economics Letters, Elsevier, Elsevier, vol. 12(1), pages 19-21.
    10. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, Springer, vol. 5(4), pages 297-323, October.
    11. Loomes, Graham & Sugden, Robert, 1982. "Regret Theory: An Alternative Theory of Rational Choice under Uncertainty," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 92(368), pages 805-24, December.
    12. María Escobar & José Moreno-Jiménez, 1997. "The Hierarchical compromise programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, Springer, vol. 5(2), pages 253-281, December.
    13. William G. Stillwell & Detlof von Winterfeldt & Richard S. John, 1987. "Comparing Hierarchical and Nonhierarchical Weighting Methods for Eliciting Multiattribute Value Models," Management Science, INFORMS, INFORMS, vol. 33(4), pages 442-450, April.
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