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Incremental Preference Elicitation with Bipolar Choquet Integrals

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Algorithmic Decision Theory (ADT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13023))

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Abstract

Preference modeling and preference learning are crucial issues in multicriteria decision-making to formulate recommendations that are tailored to the Decision Maker. In the field of multicriteria analysis, various aggregation functions have been studied to scalarize performance vectors and compare solutions. Nonetheless, most of these models do not take into account the presence of reference points in the criteria scales. Since it has been observed that decision makers may exhibit different attitudes towards aggregation depending on whether evaluations are above or below reference values, we consider here bipolar extensions of well-known aggregation models and propose incremental preference elicitation methods based on these models. In particular, we consider the elicitation of a 2-additive bipolar Choquet Integral, of a bipolar Weighted Ordered Weighted Average (WOWA), and of a non-weighted bipolar OWA. We propose a general approach that is implemented in all these cases and provide numerical tests showing its practical efficiency.

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References

  1. Beliakov, G., Calvo, T., James, S.: Aggregation functions for recommender systems. In: Ricci, F., Rokach, L., Shapira, B. (eds.) Recommender Systems Handbook, pp. 777–808. Springer, Boston (2015). https://doi.org/10.1007/978-1-4899-7637-6_23

  2. Benabbou, N., Gonzales, C., Perny, P., Viappiani, P.: Minimax regret approaches for preference elicitation with rank-dependent aggregators. EURO J. Decis. Process. 3(1), 29–64 (2015)

    Google Scholar 

  3. Benabbou, N., Perny, P., Viappiani, P.: Incremental elicitation of Choquet capacities for multicriteria choice, ranking and sorting problems. Artif. Intell. 246, 152–180 (2017)

    Google Scholar 

  4. Bourdache, N., Perny, P.: Anytime algorithms for adaptive robust optimization with OWA and WOWA. In: Rothe, J. (ed.) Algorithmic Decision Theory. ADT 2017. LNCS, vol. 10576, pp. 93–107. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67504-6_7

  5. Braziunas, D., Boutilier, C.: Minimax regret based elicitation of generalized additive utilities. In: UAI, pp. 25–32 (2007)

    Google Scholar 

  6. Chajewska, U., Koller, D., Parr, R.: Making rational decisions using adaptive utility elicitation. In: AAAI, pp. 363–369 (2000)

    Google Scholar 

  7. Galand, L., Perny, P., Spanjaard, O.: Choquet-based optimisation in multiobjective shortest path and spanning tree problems. Eur. J. Oper. Res. 204(2), 303–315 (2010)

    Google Scholar 

  8. Gonzales, C., Perny, P., Dubus, J.P.: Decision making with multiple objectives using gai networks. Artif. Intell. 175(7–8), 1153–1179 (2011)

    Google Scholar 

  9. Grabisch, M.: The application of fuzzy integrals in multicriteria decision making. Eur. J. Oper. Res. 89(3), 445–456 (1996)

    Google Scholar 

  10. Grabisch, M., Labreuche, C.: A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. Ann. Oper. Res. 175(1), 247–286 (2010)

    Google Scholar 

  11. Grabisch, M., Labreuche, C.: Bi-capacities - I: definition, Möbius transform and interaction. Fuzzy Sets Syst. 151(2), 211–236 (2005)

    Google Scholar 

  12. Grabisch, M., Labreuche, C.: Bi-capacities - II: the Choquet integral. Fuzzy Sets Syst. 151(2), 237–259 (2005)

    Google Scholar 

  13. Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation Functions, vol. 127. Cambridge University Press, Cambridge (2009)

    Google Scholar 

  14. Ha, V., Haddawy, P.: Problem-focused incremental elicitation of multi-attribute utility models. In: UAI, pp. 215–222 (1997)

    Google Scholar 

  15. Labreuche, C., Grabisch, M.: The Choquet integral for the aggregation of interval scales in multicriteria decision making. Fuzzy Sets Syst. 137(1), 11–26 (2003)

    Google Scholar 

  16. Martin, H., Perny, P.: BiOWA for preference aggregation with bipolar scales: application to fair optimization in combinatorial domains. In: Kraus, S. (ed.) Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, IJCAI 2019, Macao, China, 10–16 August 2019, pp. 1822–1828 (2019)

    Google Scholar 

  17. Martin, H., Perny, P.: New computational models for the Choquet integral. In: ECAI 2020 - 24th European Conference on Artificial Intelligence. Frontiers in Artificial Intelligence and Applications, vol. 325, pp. 147–154 (2020)

    Google Scholar 

  18. Miranda, P., Combarro, E.F., Gil, P.: Extreme points of some families of non-additive measures. Eur. J. Oper. Res. 174(3), 1865–1884 (2006)

    Google Scholar 

  19. Perny, P., Viappiani, P., Boukhatem, A.: Incremental preference elicitation for decision making under risk with the rank-dependent utility model. In: Uncertainty in Artificial Intelligence (2016)

    Google Scholar 

  20. Ramsay, J.O., et al.: Monotone regression splines in action. Stat. Sci. 3(4), 425–441 (1988)

    Google Scholar 

  21. Schmeidler, D.: Integral representation without additivity. Proc. Am. Math. Soc. 97(2), 255–261 (1986)

    Google Scholar 

  22. Tehrani, A.F., Cheng, W., Dembczynski, K., Hüllermeier, E.: Learning monotone nonlinear models using the Choquet integral. Mach. Learn. 89(1–2), 183–211 (2012)

    Google Scholar 

  23. Timonin, M.: Maximization of the Choquet integral over a convex set and its application to resource allocation problems. Ann. Oper. Res. 196(1), 543–579 (2012)

    Google Scholar 

  24. Torra, V.: The weighted OWA operator. Int. J. Intell. Syst. 12(2), 153–166 (1997)

    Google Scholar 

  25. Tversky, A., Kahneman, D.: Advances in prospect theory: cumulative representation of uncertainty. J. Risk Uncertain. 5(4), 297–323 (1992)

    Google Scholar 

  26. Wang, T., Boutilier, C.: Incremental utility elicitation with the minimax regret decision criterion, pp. 309–316 (2003)

    Google Scholar 

  27. Wang, T., Boutilier, C.: Incremental utility elicitation with the minimax regret decision criterion. In: IJCAI, vol. 3, pp. 309–316 (2003)

    Google Scholar 

  28. White III, C.C., Sage, A.P., Dozono, S.: A model of multiattribute decisionmaking and trade-off weight determination under uncertainty. IEEE Trans. Syst. Man Cybern. 14(2), 223–229 (1984)

    Google Scholar 

  29. Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)

    Google Scholar 

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Acknowledgement

We wish to thank anonymous reviewers for their useful comments on a preliminary version.

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Authors and Affiliations

  1. Sorbonne Université, CNRS, Laboratoire d’Informatique de Paris 6, LIP6, Paris, France

    Hugo Martin & Patrice Perny

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  1. Hugo Martin
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  2. Patrice Perny
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Correspondence to Hugo Martin .

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Editors and Affiliations

  1. National Technical University of Athens, Athens, Greece

    Dimitris Fotakis

  2. Consejo Superior de Investigaciones Cientificas, Madrid, Madrid, Spain

    David Ríos Insua

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Martin, H., Perny, P. (2021). Incremental Preference Elicitation with Bipolar Choquet Integrals. In: Fotakis, D., Ríos Insua, D. (eds) Algorithmic Decision Theory. ADT 2021. Lecture Notes in Computer Science(), vol 13023. Springer, Cham. https://doi.org/10.1007/978-3-030-87756-9_7

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  • DOI: https://doi.org/10.1007/978-3-030-87756-9_7

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  • Online ISBN: 978-3-030-87756-9

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