Abstract
In the previous chapters we have extensively used a geometric scale in order to model the gradations of comparative human judgement. Geometric progression seems to be reasonable but the progression factor 2 established on the basis of the categorization of time, space, light, and sound, remains questionable. The present chapter is therefore concerned with a one-parameric class of geometric scales. We analyze the behaviour of the AHP and SMART when the so-called scale parameter varies over a positive range of values. Theoretical arguments and numerical experiments with small and large problems show that the scale sensitivity of the terminal scores is low whereas the rank order remains unchanged.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References to Chapter 4
Belton, V., and Gear, A.E., “On a Shortcoming of Saaty’s Method of Analytical Hierarchies”. Omega 11, 227–230, 1983.
Dennis, A., George, R.J.F., Jessup, L.M., Nunamaker, J.F., and Vogel, D.R., “Information Technology to Support Electronic Meetings”. MIS Quarterly 12, 591–624, 1988.
DeSanctis, G., and Gallupe, R.B., “A Foundation for the Study of Group Decision Support Systems”. Management Science 33, 598–609, 1987.
Gennip, C.G.E., Hulshof, J.A.M., and Lootsma, F.A., “A Multi-Criteria Evaluation of Diseases in a Study for Public-Health Planning”. European Journal of Operational Research 99, 236–240, 1997.
Légrády, K., Lootsma, F.A., Meisner, J., and Schellemans, F., “Multi-Criteria Decision Analysis to Aid Budget Allocation”. In M. Grauer and A.P. Wierzbicki (eds.), “Interactive Decision Analysis”. Springer, Berlin, 1984, pp. 164–174.
Lootsma, F.A., “Modélisation du Jugement Humain dans l’Analyse Multicritère au Moyen de Comparaisons par Paires”. RAIRO/Recherche Opérationnelle 21, 241–257, 1987.
Lootsma, F.A., “Scale Sensitivity in the Multiplicative AHP and SMART”. Journal of Multi-Criteria Decision Analysis 2, 87–110, 1993.
Lootsma, F.A., Meisner, J., and Schellemans, F., “Multi-Criteria Decision Analysis as an Aid to the Strategic Planning of Energy R & D”. European Journal of Operational Research 25, 216–234, 1986.
Roberts, F.S., “Measurement Theory”. Addison-Wesley, Reading, Mass., 1979.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Kluwer Academic Publishers
About this chapter
Cite this chapter
(1999). Scale Sensitivity and Rank Preservation. In: Lootsma, F.A. (eds) Multi-Criteria Decision Analysis via Ratio and Difference Judgement. Applied Optimization, vol 29. Springer, Boston, MA. https://doi.org/10.1007/978-0-585-28008-0_4
Download citation
DOI: https://doi.org/10.1007/978-0-585-28008-0_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-5669-1
Online ISBN: 978-0-585-28008-0
eBook Packages: Springer Book Archive