Abstract
The pairwise comparison method is widely used to rank a finite, usually small number of decision variants especially in a case when neither a direct evaluation nor the utility theory gives satisfactory results. In this method, an expert or a group of experts is asked to provide his/their opinions concerning each pair of factors expressing a relative importance of one variant in a pair over the second one. It happens however that an expert or few experts cannot provide his/their opinions concerning a pair or pairs of factors. In such a case the resulting judgement matrices are incomplete and a problem of estimating missing data arises. The paper addresses some issues concerning lacking data. Some numerical examples are included.
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
Thurstone L.L A low of comparative judgements. Psychological Rev., 34, (1927) 273–286.
Thurstone, L.L. Psychophysical Analysis. American Journal of Psychology, 38, (1927b) 368–389.
Thurstone, L.L. The method of paired comparisons for social values. Journal of Abnormal Social Psychology, 21, (1927c) 384–400.
Saaty, T.L.: The Analytic Hierarchy Process Series I, RWS publication, 1990.
P.T. Harker, Alternative modes of questioning in the analytic hierarchy process. Mathematical Modelling 9: 3, (1987) 353–360.
S. Shiraishi and T. Obata and M. Daigo, Properties of a positive reciprocal matrix and their application to AHP, Journal of the Operations Research Society of Japan 41:3, (1998) 404–414.
P.T. Harker, Incomplete pairwise comparisons in the analytic hierarchy process. Mathematical Modelling 9: 11, (1987) 837–848.
M. Kwiesielewicz The logarithmic least squares and the generalized pseudoinverse in estimating ratios, European Journal of Operational Research, 93, (1996) 611–619.
E. van Uden, Estimating missing data in pairwise comparison matrices. Operational and Systems Research in the Face to Challenge the XXI Century, Methods and Techniques in Information Analysis and Decision Making (Z. Bubnicki, O. Hryniewicz and R. Kulikowski Eds.) Academic Printing House, Warsaw, (2002) II-73–II-80.
F. Carmone, Kara A., Zanakis S. H. A Monte Carlo Investigation of Incomplete Pairwise Comparison Matrices in AHP, European Journal of Operational Research, 102:3, (1997) 538–553.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kwiesielewicz, M., van Uden, E. (2003). Ranking Decision Variants by Subjective Paired Comparisons in Cases with Incomplete Data. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44842-X_22
Download citation
DOI: https://doi.org/10.1007/3-540-44842-X_22
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40156-8
Online ISBN: 978-3-540-44842-6
eBook Packages: Springer Book Archive