An elementary proof of Paelinck’s theorem on the convex hull of ranked criterion weights. (English) Zbl 0727.90040

Summary: J. H. P. Paelinck’s theorem [see “Qualitative multiple-criteria analysis, environmental protection and multi-regional development”, Eur. Meet. Regional Sci. Assoc., Budapest 1975, Memorandum Erasmus Univ. Rotterdam, The Netherlands (1975)] provides a simple characterization of the set of possible criterion weights when only the rank order of the criteria is known. Methods for multicriteria analysis based on this theorem are sometimes able to identify a preferred alternative without numerical estimates of these weights. We provide a new, elementary proof of the theorem.


90B50 Management decision making, including multiple objectives
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[1] Albers, L.H., Het gewichtsloze gewogen, (), (in Dutch)
[2] Ancot, J.P.; Paelinck, J.H.P., Tien jaar qualiflex, (), (in Dutch)
[3] Hinloopen, E.; Nijkamp, P.; Rietveld, P., Qualitative discrete multiple criteria choice models in regional planning, Regional science and urban economics, 13, 77-102, (1983)
[4] Israels, A.Z.; Keller, W.J., Multi-criteria analyse voor ordinale data, Kwantitatieve methoden, 7, 49-74, (1986), (in Dutch)
[5] Kok, M.; Lootsma, F.A., Pairwise comparison methods in multi-objective programming, with applications in a long-term energy-planning model, European journal of operational research, 22, 44-55, (1985) · Zbl 0578.90040
[6] Lootsma, F.A., Numerical scaling of human judgement in pairwise comparison methods for fuzzy multi-criteria decision analysis, (), 57-88
[7] Lootsma, F.A.; Meisner, J.; 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)
[8] Lootsma, F.A.; Mensch, T.C.A.; Vos, F.A., Multi-criteria analysis and budget reallocation in long-term research planning, European journal of operational research, 47, 293-305, (1990)
[9] Nijkamp, P., Multi-dimensional spatial data and decision analysis, (1979), Wiley New York
[10] Paelinck, J.H.P., Qualitative multiple-criteria analysis, environmental protection and multi-regional development, (), The Netherlands · Zbl 0429.62082
[11] ()
[12] Pulles, J.W., Beleidsanalyse Van de waterhuishouding Van nederland, (1985), Ministerie van Verkeer en Waterstaat The Hague, The Netherlands, (in Dutch)
[13] Saaty, Th.L., The analytic hierarchy process, planning, priority setting, resource allocation, (1980), McGraw-Hill New York · Zbl 0587.90002
[14] Voogd, H., Multicriteria evaluation for urban and regional planning, () · Zbl 0451.90097
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