Learning Aggregation Operators for Preference Modeling
Inhaltsverzeichnis
Reference
Vicenç Torra: Learning Aggregation Operators for Preference Modeling. In: Fürnkranz, J. and Hüllermeier, E.: Preference Learning, 2011, 317-333.
DOI
http://dx.doi.org/10.1007/978-3-642-14125-6_15
Abstract
Aggregation operators are useful tools for modeling preferences. Such operators include weighted means, OWA and WOWA operators, as well as some fuzzy integrals, e.g. Choquet and Sugeno integrals. To apply these operators in an effective way, their parameters have to be properly defined. In this chapter, we review some of the existing tools for learning these parameters from examples.
Extended Abstract
Bibtex
@incollection{
year={2011},
isbn={978-3-642-14124-9},
booktitle={Preference Learning},
editor={Fürnkranz, Johannes and Hüllermeier, Eyke},
doi={10.1007/978-3-642-14125-6_15},
title={Learning Aggregation Operators for Preference Modeling},
url={http://dx.doi.org/10.1007/978-3-642-14125-6_15, http://de.evo-art.org/index.php?title=Learning_Aggregation_Operators_for_Preference_Modeling },
publisher={Springer Berlin Heidelberg},
author={Torra, Vicenç},
pages={317-333},
language={English}
}
Used References
1. E. Armengol, F. Esteva, L. Godo, V. Torra, On learning similarity relations in fuzzy case-based reasoning, in Transactions on Rough Sets II: Rough Sets and Fuzzy Sets, Lecture Notes in Computer Science, vol. 3135, ed. by J.F. Peters, A. Skowron, D. Dubois, J. Grzymala-Busse, M. Inuiguchi, L. Polkowski (2004), pp. 14–32
2. G. Beliakov, R. Mesiar, L. Valaskova, Fitting generated aggregation operators to empirical data, Int. J. Unc. Fuzz. Knowl. Based Syst. 12, 219–236, (2004) http://dx.doi.org/10.1142/S0218488504002783
3. T. Calvo, A. Kolesárová, M. Komorníková, R. Mesiar, Aggregation operators: properties, classes and construction methods, in Aggregation Operators, ed. by T. Calvo, G. Mayor, R.Mesiar (Physica-Verlag, 2002), pp. 3–104
4. W. Edwards, Probability-preferences in gambling. Am. J. Psychol. 66, 349–364 (1953) http://dx.doi.org/10.2307/1418231
5. D.P. Filev, R.R. Yager, On the issue of obtaining OWA operator weights. Fuzzy Sets Syst. 94, 157–169 (1998) http://dx.doi.org/10.1016/S0165-0114(96)00254-0
6. J. Fodor, M. Roubens, Fuzzy Preference Modelling and Multicriteria Decision Support (Kluwer, 1994)
7. M. Grabisch, k-order additive discrete fuzzy measures and their representation. Fuzzy Sets Syst. 92(2), 167–189 (1997) http://dx.doi.org/10.1016/S0165-0114(97)00168-1
8. E. Hüllermeier, J. Fürnkranz, W. Cheng, K. Brinker, Label ranking by learning pairwise preferences. Artif. Intell. 172, 1897–1916 (2008) http://dx.doi.org/10.1016/j.artint.2008.08.002
9. T. Kamishima, H. Kazawa, S. Akaho, A survey and empirical comparison of object ranking methods, in Preference Learning, ed. by J. Fürnkranz, E. Hüllermeier (Springer, 2010)
10. E.P. Klement, R. Mesiar, E. Pap, Triangular Norms (Kluwer, 2000)
11. Y. Narukawa, V. Torra, Fuzzy measure and probability distributions: distorted probabilities. IEEE Trans Fuzzy Syst. 13(5), 617–629 (2005) http://dx.doi.org/10.1109/TFUZZ.2005.856563
12. A. Rapoport, Decision Theory and Decision Behavior (Kluwer, 1989)
13. B. Roy, Multicriteria Methodology for Decision Aiding (Kluwer, 1996)
14. M. Sugeno, Theory of Fuzzy Integrals and its Applications, Ph.D. Dissertation, Tokyo Institute of Technology, Tokyo, Japan, 1974
15. V. Torra, The weighted OWA operator. Int. J. Intel. Syst. 12, 153–166 (1997) http://dx.doi.org/10.1002/(SICI)1098-111X(199702)12%3A2%3C153%3A%3AAID-INT3%3E3.0.CO%3B2-P
16. V. Torra, On hierarchically S-decomposable fuzzy measures. Int. J. Intel. Syst. 14(9), 923–934 (1999) http://dx.doi.org/10.1002/(SICI)1098-111X(199909)14%3A9%3C923%3A%3AAID-INT5%3E3.0.CO%3B2-O
17. V. Torra, On the learning of weights in some aggregation operators. Mathware Soft Comput. 6, 249–265 (1999)MathSciNet
18. V. Torra, Learning weights for the Quasi-Weighted Mean. IEEE Trans. Fuzzy Syst. 10(5), 653–666 (2002) http://dx.doi.org/10.1109/TFUZZ.2002.803498
19. V. Torra, Y. Narukawa, Modeling decisions: information fusion and aggregation operators (Springer, 2007)
20. V. Torra, Y. Narukawa, Modelització de decisions: fusió d’informació i operadors d’agregació (UAB, 2007)
21. A. Valls, ClusDM: A Multiple Criteria Decision Making Method for Heterogeneous Data Sets (Monografies de l’IIIA, 2003)
22. A. Verkeyn, D. Botteldooren, B. De Baets, G. De Tré, Sugeno integrals for the modelling of noise annoyance aggregation, in Proceedings of the 10th IFSA Conference, Lecture Notes in Artificial Intelligence, vol.2715 (2003), pp. 277–284
23. S. Weber,⊥-decomposable measures and integrals for archimedean t-conorms⊥. J. Math. Anal. Appl. 101, 114–138 (1984) http://dx.doi.org/10.1016/0022-247X(84)90061-1
24. R.R. Yager, On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans. Syst. Man Cybern. 18, 183–190 (1988) http://dx.doi.org/10.1109/21.87068
