Abstract
We state a celebrated theorem due to Strassen (1965) and derive from it Meyer’s (1966) characterization of dilation kernels. It is shown that the latter result and thus Strassen’s theorem provides a useful tool for deriving characterizations of certain orderings. As an example we prove a famous result due to Hardy/Littlewood/Pólya 1934, 1952. Finally we state some applications in the field of OWA-operators.
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
Basile, L., L.D’ Apuzzo, Orderingsfor classes of aggregation operators. Uncertainty, Fuzziness, and Knowledge-Based Systems 1996,4, 145–156.
Blackwell. D., Equivalent comparison of experiments. Ann. Math. Stat. 1953, 24, 265–272.
Fodor, J., J.L. Marichal, M. Roubens, Characterization of the ordered-weighted averaging operators. To appear (199?).
Hardy, G.H., J.E. Littlewood, G. Pólya, Inequalities. Cambridge University Press, 1934/52.
Meyer, P.R., Probability and Potential. Blaisdell, 1966.
Ralescu, A.L., D.A. Ralescu, Extensions of fuzzy aggregation. To appear (199?).
Schmeidler, D., Integral representation without additivity. Proc. AMS 1986, 97,255–261.
Skala, H.J., Concerning ordered weighted averaging aggregation operators. Statistical Papers 1991, 32, 35–44.
Skala, H.J., The existence of probability measures with given marginals. Ann. Prob. 1993, 21, 136–142.
Skala, H.J., On a representation theorem ofSchmeidler. To appear in Statistical Papers (199?).
Strassen, V., The existence of probability measures with given marginals. Ann. Math. Stat. 1965, 36, 423–439.
Yager, R.R., On ordered weighted averaging aggregation operators in multicriteria decision making. I.E.E.E., Transactions on Systems, Man, and Cybernetics 1988,18,1, 183–190.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Skala, H.J. (1997). Useful Tools for Aggregation Procedures: Some Consequences and Applications of Strassen’s Measurable Hahn-Banach-Theorem. In: Yager, R.R., Kacprzyk, J. (eds) The Ordered Weighted Averaging Operators. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6123-1_8
Download citation
DOI: https://doi.org/10.1007/978-1-4615-6123-1_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7806-8
Online ISBN: 978-1-4615-6123-1
eBook Packages: Springer Book Archive