The Analytic Hierarchy Process (AHP) of Saaty (1980) is a widely used method for MCDA, presumably because it efcitates preference information from the decision makers in a manner which they find easy to understand. The basic step is the pairwise comparison of two so-called stimuli, two alternatives under a given criterion, for instance, or two criteria. The decision maker is requested to state whether he/she is indifferent between the two stimuli or whether he/she has a weak, strict, strong, or very strong preference for one of them. The original AHP has been criticized because the algorithmic steps do not properly take into account that the method is based upon ratio information. The shortcomings can easily be avoided in the Additive and the Multiplicative ARP to be discussed in the present chapter. The Additive AHP is the SMART procedure with pairwise comparisons on the basis of difference information. The Multiplicative ARP with pairwise comparisons on the basis of ratio information is a variant of the original AHP. There is a logarithmic relationship between the two methods that we will extensively employ in the elicitation of preference information.


Decision Maker Analytic Hierarchy Process Criterion Weight Indifference Curve Impact Score 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References to Chapter 3

  1. 1.
    Bana e Costa, C.A., and Vansnick, J.C., “A Theoretical Framework for Measuring Attractiveness by a Category Based Evaluation Technique (MACBETH)”. In J. Climaco (ed.), “Multicriteria Analysis”, Springer, Berlin, 1997, pp. 15–24.Google Scholar
  2. 2.
    Barzilai, J., Cook, W.D., and Golany, B., “Consistent Weights for Judgement Matrices of the Relative Importance of Alternatives”. Operations Research Letters 6, 131–134, 1987.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Barzilai, J., and Golany, B., “Deriving Weights from Pairwise Comparison Matrices: the Additive Case”. Operations Research Letters 9, 407–410, 1990.MATHCrossRefGoogle Scholar
  4. 4.
    Barzilai, J., and Golany, B., “AHP Rank Reversal, Normalization, and Aggregation Rules”. INFOR 32, 57–64, 1994.MATHGoogle Scholar
  5. 5.
    Barzilai, J., and Lootsma, F.A., “Power Relations and Group Aggregation in the Multiplicative AHP and SMART”. Journal of Multi-Criteria Decision Analysis 6, 155–165, 1997. In the same issue there are comments by O. Larichev (166), P. Korhonen (167–168), and L. Vargas (169–170), as well as a response by F.A. Lootsma and J. Barzilai (171–174).MATHCrossRefGoogle Scholar
  6. 6.
    Belton, V., and Gear, A.E., “On a Shortcoming of Saaty’s Method of Analytical Hierarchies”. Omega 11, 227–230, 1983.CrossRefGoogle Scholar
  7. 7.
    Borcherding, K., and Winterfeldt, D. von, “The Effect of Varying Value Trees on Multi-attribute Evaluations”. Acta Psychologica 68, 153–170, 1988.CrossRefGoogle Scholar
  8. 8.
    Bradley, R.A., and Terry, M.E., “The Rank Analysis of Incomplete Block Designs. I. The Method of Paired Comparisons”. Biometrika 39, 324–345, 1952.MATHMathSciNetGoogle Scholar
  9. 9.
    Brun, W., and Teigen, K.H., “Verbal Probabilities: Ambiguous, Context-Dependent, or Both?”. Organizational Behavior and Human Decision Processes 41, 390–404, 1988.CrossRefGoogle Scholar
  10. l0.
    Budescu, D.V., Crouch, B.D., and Morera, O.F., “A Multi-Criteria Comparison of Response Scales and Scaling Methods in the AHP”. In W.C. Wedley (ed.), Proceedings of the Fourth International Symposium on the AHP. Simon Fraser University, Burnaby, B.C., Canada, 1996, pp. 280–291.Google Scholar
  11. 11.
    Cogger, K.O., and Yu, P.L., “Eigenweight Vectors and Least-Distance Approximations for Revealed Preferences in Pairwise Weight Ratios”. Journal of Optimization Theory and Applications 46, 483–491, 1985.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Crawford, G., and Williams, C., “A Note on the Analysis of Subjective Judgement Matrices”. Journal of Mathematical Psychology 29, 387–405, 1985.MATHCrossRefGoogle Scholar
  13. 13.
    David, H.A., “The Method of Paired Comparisons”. Griffin, London, 1963.Google Scholar
  14. 14.
    Dyer, J.S., “Remarks on the Analytic Hierachy Process”. Management Science 36, 249–258, 1990. In the same issue there are apologies by T.L. Saaty (259–268), P.T. Harker and L. Vargas (269–273), and a further clarification by J.S. Dyer (274–275).CrossRefMathSciNetGoogle Scholar
  15. 15.
    French, S., “Decision Theory, an Introduction to the Mathematics of Rationality”. Ellis Horwood, Chichester, 1988.MATHGoogle Scholar
  16. 16.
    Johnson, C.R., Beine, W.B., and Wang, T.J., “Right-Left Asymmetry in an Eigenvector Ranking Procedure”. Journal of Mathematical Psychology 19, 61–64, 1979.CrossRefMathSciNetGoogle Scholar
  17. 17.
    Keeney, R., and Raiffa, H., “Decisions with Multiple Objectives: Preferences and Value Trade-offs”. Wiley, New York, 1976.Google Scholar
  18. 18.
    Lootsma, F.A., “Saaty’s Priority Theory and the Nomination of a Senior Professor in Operations Research”. European Journal of Operational Research 4, 380–388, 1980.CrossRefGoogle Scholar
  19. 19.
    Lootsma, F.A., “Modélisation du Jugement Humain dans l’Analyse Multicritère au Moyen de Comparaisons par Paires”. RAIRO/Recherche Opérationnelle 21, 241–257, 1987.MATHMathSciNetGoogle Scholar
  20. 20.
    Lootsma, F.A., “Scale Sensitivity in the Multiplicative AHP and SMART”. Journal of Multi-Criteria Decision Analysis 2, 87–110, 1993.MATHCrossRefGoogle Scholar
  21. 21.
    Lootsma, F.A., “Multi-Criteria Decision Analysis in a Decision Tree”. European Journal of Operational Research 101, 442–451, 1997.MATHCrossRefGoogle Scholar
  22. 22.
    Lootsma, F.A., Boonekamp, P.G.M., Cooke, R.M., and Oostvoorn, F. van, “Choice of a Long-Term Strategy for the National Electricity Supply via Scenario Analysis and Multi-Criteria Analysis”. European Journal of Operational Research 48, 189–203, 1990.CrossRefGoogle Scholar
  23. 23.
    Mintzberg, H., “Power in and around Organizations”. Prentice-Hall, Englewood Cliffs, N.J., 1983.Google Scholar
  24. 24.
    Pöyhönen, M., and Hämäläinen, R.P., “Notes on the Weighting Biases in Value Trees”. To appear in the Journal of Behavioural Decision Making, 1998.Google Scholar
  25. 25.
    Ramanathan, R., “A Note on the Use of Goal Programming for the Multiplicative AHP”. Journal of Multi-Criteria Decision Analysis 6, 296–307, 1997.MATHCrossRefGoogle Scholar
  26. 26.
    Saaty, T.L., “A Scaling Method for Priorities in Hierarchical Structures”. Journal of Mathematical Psychology 15, 234–281, 1977.MATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Saaty, T.L., “The Analytic Hierarchy Process, Planning, Priority Setting, and Resource Allocation”. McGraw-Hill, New York, 1980.Google Scholar
  28. 28.
    Saaty, T.L., and Vargas, L.G., “Inconsistency and Rank Preservation”. Journal of Mathematical Psychology 28, 205–214, 1984.MATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Stewart, T.J., “A Critical Survey on the Status of Multi-Criteria Decision Making Theory and Practice”. Omega 20, 569–586, 1992.CrossRefGoogle Scholar
  30. 30.
    Takeda, E., Cogger, K.O., and Yu, P.L., “Estimating Criterion Weights using Eigenvectors: a Comparative Study”. Omega 20, 569–586, 1987.Google Scholar
  31. 31.
    Teigen, K.H., “When are Low-Probability Events judged to be Probable?. Effects of Outcome-Set Characteristics on Verbal Probability Estimates”. Acta Psychologica 67, 157–174, 1988.CrossRefGoogle Scholar
  32. 32.
    Thurstone, L.L., “The Method of Paired Comparisons for Social Values”. Journal of Abnormal Psychology 21, 384–400, 1927.CrossRefGoogle Scholar
  33. 33.
    Torgerson, W.S., “Distances and Ratios in Psycho-Physical Scaling”. Acta Psychologica XIX, 201–205, 1961.Google Scholar
  34. 34.
    Triantaphyllou, E., Lootsma, F.A., Pardalos, P.M., and Mann, S.H., “On the Evaluation and Application of Different Scales for Quantifying Pairwise Comparisons in Fuzzy Sets”. Journal of Multi-Criteria Decision Analysis 3, 133–155, 1994.MATHCrossRefGoogle Scholar
  35. 35.
    Winterfeldt, D. von, and Edwards, W., “Decision Analysis and Behavioral Research”. Cambridge University Press, Cambridge, UK, 1986.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Personalised recommendations