Abstract
In this paper, we deal with the problem of modelling preferences in multiple criteria evaluation situations. When the number of objects to be evaluated is small, then it is possible to make a detailed analysis of the decision-maker’s preferences to find out a “value” or a “score” for each object. For example, in the Analytic Hierarchy Process, preference analysis is based on pairwise comparisons. We consider the statistical analysis of pairwise comparisons, and show that several issues of measurement scale must be clearly understood, before one can reliably apply the methods in practice. Our approach is based on the use of regression analysis rather than the eigenvalue technique of the AHP, to find the value scores for alternatives.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Alho, J.M., Kangas, J. and Kolehmainen, O., 1996: Uncertainty in expert predictions of the ecological consequences of forest plans. Applied Statistics 45: 1 - 14.
Alho, J.M. and Kangas, J., 1997: Analyzing uncertainties in experts opinions of forest plan performance. Forest Science 43: 521 - 528.
Alho, J.M., Kolehmainen, O. and Leskinen, P., 2001: Regression methods for pairwise comparisons data. In D.L. Schmoldt, J. Kangas, G.A. Mendoza and M. Pesonen (eds.), The Analytic Hierarchy Process in Natural Resource and Environmental Decision Making. Kluwer Academic Publishers, p. 235 - 251.
Bana e Costa, C.A. and Vansnick, J.C., 1999: The MACBETH approach: basic ideas, software and an application. In N. Meskens and M. Roubens (eds.), Advances in Decision Analysis. Kluwer Academic Publishers, p. 131 - 157.
Barzilai, J., Cook, W. and Golany, B., 1987: Consistent weights for judgements matrices of the relative importance for alternatives. Operations Research Letters 6: 131 - 134.
Carriere, J. and Finster, M., 1992: Statistical theory for the ratio model of paired comparisons. Journal of Mathematical Psychology 36: 450 - 460.
Chang, S. and Buongiorno, J., 1981: A programming model for multiple use forestry. Journal of Environmental Management 13: 45 - 58.
Crawford, G. and Williams, C., 1985: A note on the analysis of subjective judgment matrices. Journal of Mathematical Psychology 29: 387 - 405.
De Jong, P., 1984: A statistical approach to Saatys scaling method for priorities. Journal of Mathematical Psychology 28: 467 - 478.
Gantmacher, F.R., 1959: The Theory of Matrices. Vol. II, Chelsea, New York.
Hinloopen, E., Nijkamp, P. and Rietveld, P., 1983: The regime method: a new multicriteria technique. In P. Hansen (ed.), Essays and Surveys on Multiple Criteria Decision Making. Springer, p. 146 - 155.
Keeney, R. and Raiffa, H., 1976: Decisions with Multiple Objectives. Wiley, New York.
Korhonen, P., Wallenius, J. and Zionts, S., 1984: Solving the discrete multiple criteria problem using convex cones. Management Science 30: 1336 - 1345.
Korhonen, P., 1986: A hierarchical interactive method for ranking alternatives with multiple qualitative criteria. European Journal of Operational Research 24: 265 - 276.
Korhonen, P., 1988: A visual reference direction approach to solving discrete multiple criteria problems. European Journal of Operational Research 34: 152 - 159.
Korhonen, P. and Karaivanova, J., 1999: An algorithm for projecting a reference direction onto the nondominated set of given points. In IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 29: 429 - 435.
Leskinen, P. and Kangas, J., 1998: Analysing uncertainties of interval judgment data in multiple-criteria evaluation of forest plans. Silva Fennica 32: 363 - 372.
Leskinen, P., 2000: Measurement scales and scale independence in the Analytic Hierarchy Process. Journal of Multi-Criteria Decision Analysis 9: 163 - 174.
Leskinen, P., 2001: Statistical Methods for Measuring Preferences. University of Joensuu, Publications of Social Sciences 48.
Lootsma, F.A., 1991: Scale Sensitivity and Rank Preservation in a Multiplicative Variant of the AHP and SMART. Report 91-67, Faculty of Technical Mathematics and Informatics, Delft University of Technology, Delft, The Netherlands.
Lootsma, F.A., 1993: Scale sensitivity in the multiplicative AHP and SMART. Journal of Multi-Criteria Decision Analysis 2: 87 - 110.
Lotfi, V., Stewart, T.J. and Zionts, S., 1992: An aspiration-level interactive model for multiple criteria decision making Computers and Operations Research 19: 671 - 681.
Ma, D. and Zheng, X., 1991: 9/9-9/1 scale method of AHP. In Proceedings of the 2nd International Symposium on the AHP. Vol. I, University of Pittsburgh, Pittsburgh, PA, p. 197 - 202.
Olson, D., 1996: Decision Aids for Selection Problems. Springer Series in Operations Research, New York.
Roy, B., 1973: How outranking relation helps multiple criteria decision making. In J. Cochrane and M. Zeleny (eds.), Multiple Criteria Decision Making. University of South Carolina Press, Columbia, SC, p. 179 - 201.
Saaty, T.L., 1977: A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology 15: 234 - 281.
Saaty, T.L., 1980: The Analytic Hierarchy Process. Planning, Priority Setting, Resource Allocation. McGraw-Hill, New York.
Saaty, T.L. and Vargas, F., 1984: Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios. Mathematical Modelling 5: 309-324,
Salo, A.A. and Hämäläinen, R.P., 1997: On the measurement of preferences in the Analytic Hierarchy Process. Journal of Multi-Criteria Decision Analysis 6: 309 - 319.
Zhang, S.-S. and Genest, C., 1996: Etude dun test de confirmation des priorités dans le cadre dur procédé danalyse hiérarchique. Revue de Statistique Appliquée 44: 81 - 103.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Alho, J.M., Korhonen, P., Leskinen, P. (2002). Measurement of Preferences in Multiple Criteria Evaluation. In: Pukkala, T. (eds) Multi-objective Forest Planning. Managing Forest Ecosystems, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9906-1_2
Download citation
DOI: https://doi.org/10.1007/978-94-015-9906-1_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6207-9
Online ISBN: 978-94-015-9906-1
eBook Packages: Springer Book Archive