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Learning Aggregation Operators for Preference Modeling

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Preference Learning

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.

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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

    Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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

    Google Scholar 

  4. W. Edwards, Probability-preferences in gambling. Am. J. Psychol. 66, 349–364 (1953)

    Article  Google Scholar 

  5. D.P. Filev, R.R. Yager, On the issue of obtaining OWA operator weights. Fuzzy Sets Syst. 94, 157–169 (1998)

    Article  MathSciNet  Google Scholar 

  6. J. Fodor, M. Roubens, Fuzzy Preference Modelling and Multicriteria Decision Support (Kluwer, 1994)

    Google Scholar 

  7. M. Grabisch, k-order additive discrete fuzzy measures and their representation. Fuzzy Sets Syst. 92(2), 167–189 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  8. E. Hüllermeier, J. Fürnkranz, W. Cheng, K. Brinker, Label ranking by learning pairwise preferences. Artif. Intell. 172, 1897–1916 (2008)

    Article  MATH  Google Scholar 

  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)

    Google Scholar 

  10. E.P. Klement, R. Mesiar, E. Pap, Triangular Norms (Kluwer, 2000)

    Google Scholar 

  11. Y. Narukawa, V. Torra, Fuzzy measure and probability distributions: distorted probabilities. IEEE Trans Fuzzy Syst. 13(5), 617–629 (2005)

    Article  MathSciNet  Google Scholar 

  12. A. Rapoport, Decision Theory and Decision Behavior (Kluwer, 1989)

    Google Scholar 

  13. B. Roy, Multicriteria Methodology for Decision Aiding (Kluwer, 1996)

    Google Scholar 

  14. M. Sugeno, Theory of Fuzzy Integrals and its Applications, Ph.D. Dissertation, Tokyo Institute of Technology, Tokyo, Japan, 1974

    Google Scholar 

  15. V. Torra, The weighted OWA operator. Int. J. Intel. Syst. 12, 153–166 (1997)

    Article  MATH  Google Scholar 

  16. V. Torra, On hierarchically S-decomposable fuzzy measures. Int. J. Intel. Syst. 14(9), 923–934 (1999)

    Article  MATH  Google Scholar 

  17. V. Torra, On the learning of weights in some aggregation operators. Mathware Soft Comput. 6, 249–265 (1999)

    MathSciNet  Google Scholar 

  18. V. Torra, Learning weights for the Quasi-Weighted Mean. IEEE Trans. Fuzzy Syst. 10(5), 653–666 (2002)

    Article  MathSciNet  Google Scholar 

  19. V. Torra, Y. Narukawa, Modeling decisions: information fusion and aggregation operators (Springer, 2007)

    Google Scholar 

  20. V. Torra, Y. Narukawa, Modelització de decisions: fusió d’informació i operadors d’agregació (UAB, 2007)

    Google Scholar 

  21. A. Valls, ClusDM: A Multiple Criteria Decision Making Method for Heterogeneous Data Sets (Monografies de l’IIIA, 2003)

    Google Scholar 

  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

    Google Scholar 

  23. S. Weber,⊥-decomposable measures and integrals for archimedean t-conorms⊥. J. Math. Anal. Appl. 101, 114–138 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  24. R.R. Yager, On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans. Syst. Man Cybern. 18, 183–190 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  25. http://www.mdai.cat/ifao/ifao.models.r

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Acknowledgements

Partial support by the Generalitat de Catalunya (2005 SGR 00446 and 2005-SGR-00093) and by the Spanish MEC (projects ARES – CONSOLIDER INGENIO 2010 CSD2007-00004 – and eAEGIS – TSI2007-65406-C03-02) is acknowledged.

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Authors and Affiliations

  1. IIIA, Artificial Intelligence Research Institute, CSIC, Spanish National Research Council, Campus UAB s/n 08193 Bellaterra, Catalonia, Spain

    Vicenç Torra

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  1. Vicenç Torra
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Correspondence to Vicenç Torra .

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Editors and Affiliations

  1. FB Informatik, TU Darmstadt, Hochschulstr. 10, Darmstadt, 64289, Germany

    Johannes Fürnkranz

  2. FB Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Str., Marburg, 35032, Germany

    Eyke Hüllermeier

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Torra, V. (2010). Learning Aggregation Operators for Preference Modeling. In: Fürnkranz, J., Hüllermeier, E. (eds) Preference Learning. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14125-6_15

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  • DOI: https://doi.org/10.1007/978-3-642-14125-6_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14124-9

  • Online ISBN: 978-3-642-14125-6

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