Abstract
In multi-criteria decision making, it is necessary to aggregate (combine) utility values corresponding to several criteria (parameters). The simplest way to combine these values is to use linear aggregation. In many practical situations, however, linear aggregation does not fully adequately describe the actual decision making process, so non-linear aggregation is needed.
From the purely mathematical viewpoint, the next natural step after linear functions is the use of quadratic functions. However, in decision making, a different type of non-linearities are usually more adequate than quadratic ones: non-linearities like OWA or Choquet integral that use min and max in addition to linear combinations. In this paper, we explain the empirically observed advantage of such aggregation operations.
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References
Ceberio, M., Modave, F.: An interval-valued, 2-additive Choquet integral for multi-cruteria decision making. In: Proceedings of the 10th Conf. on Information Processing and Management of Uncertainty in Knowledge-based Systems IPMU 2004, Perugia, Italy (July 2004)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press, Cambridge (2001)
Feynman, R., Leighton, R., Sands, M.: Feynman Lectures on Physics. Addison-Wesley, Reading (2005)
Grabisch, M., Murofushi, T., Sugeno, M. (eds.): Fuzzy Measures and Integrals. Physica-Verlag, Heidelberg (2000)
Keeney, R.L., Raiffa, H.: Decisions with Multiple Objectives. John Wiley and Sons, New York (1976)
Luce, R.D., Raiffa, H.: Games and Decisions: Introduction and Critical Survey. Dover, New York (1989)
Raiffa, H.: Decision Analysis. Addison-Wesley, Reading (1970)
Rockafeller, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
Yager, R.R., Kacprzyk, J. (eds.): The Ordered Weighted Averaging Operators: Theory and Applications. Kluwer, Norwell (1997)
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© 2008 Springer-Verlag Berlin Heidelberg
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Modave, F., Ceberio, M., Kreinovich, V. (2008). Choquet Integrals and OWA Criteria as a Natural (and Optimal) Next Step after Linear Aggregation: A New General Justification. In: Gelbukh, A., Morales, E.F. (eds) MICAI 2008: Advances in Artificial Intelligence. MICAI 2008. Lecture Notes in Computer Science(), vol 5317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88636-5_70
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DOI: https://doi.org/10.1007/978-3-540-88636-5_70
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88635-8
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