Advertisement

Abstract

It is commonly acknowledged that a rational decision maker acts with respect to his/her value system so as to make the best decision. Confrontation of the value system of the decision maker with characteristics of possible decisions (objects) results in expression of preferences of the decision maker on the set of possible decisions. In order to support the decision maker, one must identify his/her preferences and recommend the most-preferred decision concerning either classification, or choice, or ranking. In this paper, we review multiple attribute and multiple criteria decision problems, as well as preference discovery from data describing some past decisions of the decision maker. The considered preference model has the form of a set of “if..., then...” decision rules induced from the data. To structure the data prior to induction, we use the Dominance-based Rough Set Approach (DRSA). DRSA is a methodology for reasoning about ordinal data, which extends the classical rough set approach by handling background knowledge about ordinal evaluations of objects and about monotonic relationships between these evaluations. The paper starts with an introduction to preference modeling in multiple attribute and multiple criteria decision problems, then presents the principles of DRSA, together with a didactic example, and concludes with a summary of characteristic features of DRSA in the context of preference modeling.

Keywords

Decision Rule Preference Model Multiple Criterion Decision Decision Class Monotonicity Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dembczyński, K., Greco, S., Kotłowski, W., Słowiński, R.: Statistical model for rough set approach to multicriteria classification. In: Kok, J.N., Koronacki, J., Lopez de Mantaras, R., Matwin, S., Mladenič, D., Skowron, A. (eds.) PKDD 2007. LNCS (LNAI), vol. 4702, pp. 164–175. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Dembczyński, K., Greco, S., Słowiński, R.: Rough set approach to multiple criteria classication with imprecise evaluations and assignments. European Journal of Operational Research 198, 626–636 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Dembczyński, K., Kotłowski, W., Słowiński, R.: Ordinal classification with decision rules. In: Raś, Z.W., Tsumoto, S., Zighed, D.A. (eds.) MCD 2007. LNCS (LNAI), vol. 4944, pp. 169–181. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Dembczyński, K., Kotłowski, W., Słowiński, R.: Ensemble of decision rules for ordinal classification with monotonicity constraints. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS (LNAI), vol. 5009, pp. 260–267. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Figueira, J., Greco, S., Ehrgott, M. (eds.): Multiple Criteria Decision Analysis: State of the Art Surveys. Springer, Berlin (2005)zbMATHGoogle Scholar
  6. 6.
    Figueira, J., Greco, S., Słowiński, R.: Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP method. European Journal of Operational Research 195, 460–486 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Fortemps, Ph., Greco, S., Słowiński, R.: Multicriteria decision support using rules that represent rough-graded preference relations. European Journal of Operational Research 188, 206–223 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Frank, E., Hall, M.: A simple approach to ordinal classification. In: Flach, P.A., De Raedt, L. (eds.) ECML 2001. LNCS (LNAI), vol. 2167, pp. 145–156. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. 9.
    Freund, Y., Iyer, R., Schapire, R.E., Singer, Y.: An efficient boosting algorithm for combining preferences. Journal of Machine Learning Research 6, 933–969 (2003)zbMATHGoogle Scholar
  10. 10.
    Fürnkranz, J., Hüllermeier, E.: Pairwise preference learning and ranking. In: Lavrač, N., Gamberger, D., Todorovski, L., Blockeel, H. (eds.) ECML 2003. LNCS (LNAI), vol. 2837, pp. 145–156. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. 11.
    Giove, S., Greco, S., Matarazzo, B., Słowiński, R.: Variable consistency monotonic decision trees. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 247–254. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  12. 12.
    Greco, S., Inuiguchi, M., Słowiński, R.: Dominance-based rough set approach using possibility and necessity measures. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 85–92. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  13. 13.
    Greco, S., Inuiguchi, M., Słowiński, R.: A new proposal for rough fuzzy approximations and decision rule representation. In: Peters, J.F., Skowron, A., Dubois, D., Grzymała-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds.) Transactions on Rough Sets II. LNCS, vol. 3135, pp. 319–342. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  14. 14.
    Greco, S., Inuiguchi, M., Słowiński, R.: Fuzzy rough sets and multiple-premise gradual decision rules. International Journal of Approximate Reasoning 41, 179–211 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Greco, S., Matarazzo, B., Słowiński, R.: A new rough set approach to evaluation of bankruptcy risk. In: Zopounidis, C. (ed.) Operational Tools in the Management of Financial Risks, pp. 121–136. Kluwer Academic Publishers, Dordrecht (1998)CrossRefGoogle Scholar
  16. 16.
    Greco, S., Matarazzo, B., Słowiński, R.: The use of rough sets and fuzzy sets in MCDM. In: Gal, T., Stewart, T., Hanne, T. (eds.) Advances in Multiple Criteria Decision Making, ch. 14, pp. 14.1–14.59. Kluwer Academic Publishers, Boston (1999)Google Scholar
  17. 17.
    Greco, S., Matarazzo, B., Słowiński, R.: Dealing with missing data in rough set analysis of multi-attribute and multi-criteria decision problems. In: Zanakis, S.H., Doukidis, G., Zopounidis, C. (eds.) Decision Making: Recent Developments and Worldwide Applications, pp. 295–316. Kluwer, Dordrecht (2000)CrossRefGoogle Scholar
  18. 18.
    Greco, S., Matarazzo, B., Słowiński, R.: A fuzzy extension of the rough set approach to multicriteria and multiattribute sorting. In: Fodor, J., De Baets, B., Perny, P. (eds.) Preferences and Decisions under Incomplete Information, pp. 131–154. Physica-Verlag, Heidelberg (2000)CrossRefGoogle Scholar
  19. 19.
    Greco, S., Matarazzo, B., Słowiński, R.: Rough sets theory for multicriteria decision analysis. European Journal of Operational Research 129, 1–47 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Greco, S., Matarazzo, B., Słowiński, R.: Preference representation by means of conjoint measurement & decision rule model. In: Bouyssou, D., Jacquet-Lagrèze, E., Perny, P., Słowiński, R., Vanderpooten, D., Vincke, P. (eds.) Aiding Decisions with Multiple Criteria–Essays in Honor of Bernard Roy, pp. 263–313. Kluwer, Dordrecht (2002)CrossRefGoogle Scholar
  21. 21.
    Greco, S., Matarazzo, B., Słowiński, R.: Axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough-set decision rules. European Journal of Operational Research 158, 271–292 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Greco, S., Matarazzo, B., Słowiński, R.: Dominance-Based Rough Set Approach to Knowledge Discovery (I) - General Perspective (II) - Extensions and Applications. In: Zhong, N., Liu, J. (eds.) Intelligent Technologies for Information Analysis, ch. 20 & 21, pp. 513–612. Springer, Berlin (2004)CrossRefGoogle Scholar
  23. 23.
    Greco, S., Matarazzo, B., Słowiński, R.: Decision rule approach. In: Figueira, J., Greco, S., Ehrgott, M. (eds.) Multiple Criteria Decision Analysis: State of the Art Surveys, ch. 13, pp. 507–563. Springer, Berlin (2005)CrossRefGoogle Scholar
  24. 24.
    Greco, S., Matarazzo, B., Słowiński, R.: Dominance-based rough set approach to case-based reasoning. In: Torra, V., Narukawa, Y., Valls, A., Domingo-Ferrer, J. (eds.) MDAI 2006. LNCS (LNAI), vol. 3885, pp. 7–18. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  25. 25.
    Greco, S., Matarazzo, B., Słowiński, R.: Dominance-based rough set approach as a proper way of handling graduality in rough set theory. In: Peters, J.F., Skowron, A., Marek, V.W., Orłowska, E., Słowiński, R., Ziarko, W.P. (eds.) Transactions on Rough Sets VII. LNCS, vol. 4400, pp. 36–52. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  26. 26.
    Greco, S., Matarazzo, B., Słowiński, R.: Dominance-based Rough Set Approach to Interactive Multiobjective Optimization. In: Branke, J., Deb, K., Miettinen, K., Słowiński, R. (eds.) Multiobjective Optimization: Interactive and Evolutionary Approaches, ch. 5, pp. 121–156. Springer, Berlin (2008)CrossRefGoogle Scholar
  27. 27.
    Greco, S., Matarazzo, B., Słowiński, R.: Granular Computing for Reasoning About Ordered Data: the Dominance-based Rough Set Approach. In: Pedrycz, W., Skowron, A., Kreinovich, V. (eds.) Handbook of Granular Computing, pp. 347–373. Wiley, Chichester (2008)CrossRefGoogle Scholar
  28. 28.
    Greco, S., Matarazzo, B., Słowiński, R.: Dominance-based rough set approach to decision under uncertainty and time preference. Annals of Operations Research (2009), DOI:10.1007/s10479-009-0566-8Google Scholar
  29. 29.
    Greco, S., Mousseau, V., Słowiński, R.: Ordinal regression revisited: multiple criteria ranking using a set of additive value functions. European Journal of Operational Research 191, 415–435 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Greco, S., Słowiński, R., Figueira, J., Mousseau, V.: Robust ordinal regression. In: Ehrgott, M., Figueira, J., Greco, S. (eds.) New Advances in Multiple Criteria Decision Analysis. Springer, Berlin (2009)Google Scholar
  31. 31.
    Greco, S., Pawlak, Z., Słowiński, R.: Can Bayesian confirmation measures be useful for rough set decision rules? Engineering Applications of Artificial Intelligence 17, 345–361 (2004)CrossRefGoogle Scholar
  32. 32.
    Herbrich, R., Graepel, T., Obermayer, K.: Regression models for ordinal data: a machine learning approach, Technical report TR-99/03, TU Berlin (1999)Google Scholar
  33. 33.
    Kotłowski, W., Dembczyński, K., Greco, S., Słowiński, R.: Stochastic Dominance-based Rough Set Model for Ordinal Classification. Information Sciences 178, 4019–4037 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Langley, P., Simon, H.A.: Fielded applications of machine learning. In: Michalski, R.S., Bratko, I., Kubat, M. (eds.) Machine Learning and Data Mining, pp. 113–129. Wiley, New York (1998)Google Scholar
  35. 35.
    March, J.G.: Bounded rationality, ambiguity, and the engineering of choice. In: Bell, D.E., Raiffa, H., Tversky, A. (eds.) Decision Making, Descriptive, Normative and Prescriptive Interactions, pp. 33–58. Cambridge University Press, New York (1988)CrossRefGoogle Scholar
  36. 36.
    Michalski, R.S.: A Theory and Methodology of Inductive Learning. In: Michalski, R.S., Carbonell, J.G., Mitchell, T.M. (eds.) Machine Learning: An Artificial Intelligence Approach, pp. 83–129. Tioga Publishing, Palo Alto (1983)CrossRefGoogle Scholar
  37. 37.
    Mousseau, V., Słowiński, R.: Inferring an ELECTRE TRI model from assignment examples. Journal of Global Optimization 12, 157–174 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht (1991)CrossRefzbMATHGoogle Scholar
  39. 39.
    Pawlak, Z., Słowiński, R.: Rough set approach to multi-attribute decision analysis. European Journal of Operational Research 72, 443–459 (1994)CrossRefzbMATHGoogle Scholar
  40. 40.
    Rennie, J., Srebro, N.: Loss functions for preference levels: regression with discrete ordered labels. In: Proc. of the IJCAI-2005 Multidisciplinary Workshop on Advances in Preference Handling (2005)Google Scholar
  41. 41.
    Roy, B.: Multicriteria Methodology for Decision Aiding. Kluwer Academic Publishers, Dordrecht (1996)CrossRefzbMATHGoogle Scholar
  42. 42.
    Roy, B., Bouyssou, D.: Aide Multicritère à la Décision: Méthodes et Cas. Economica, Paris (1993)Google Scholar
  43. 43.
    Shoemaker, P.J.H.: The expected utility model: its variants, purposes, evidence and limitations. Journal of Economic Literature 20, 529–562 (1982)Google Scholar
  44. 44.
    Słowiński, R.: Rough set learning of preferential attitude in multi-criteria decision making. In: Komorowski, J., Raś, Z.W. (eds.) ISMIS 1993. LNCS, vol. 689, pp. 642–651. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  45. 45.
    Słowiński, R., Greco, S., Matarazzo, B.: Axiomatization of utility, outranking and decision-rule preference models for multiple-criteria classification problems under partial inconsistency with the dominance principle. Control and Cybernetics 31, 1005–1035 (2002)zbMATHGoogle Scholar
  46. 46.
    Słowiński, R., Greco, S., Matarazzo, B.: Rough set based decision support. In: Burke, E.K., Kendall, G. (eds.) Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, ch. 16, pp. 475–527. Springer, New York (2005)Google Scholar
  47. 47.
    Słowiński, R., Greco, S., Matarazzo, B.: Rough Sets in Decision Making. In: Meyers, R. (ed.) Encyclopedia of Complexity and Systems Science. Springer, New York (2009)Google Scholar
  48. 48.
    Srebro, N., Rennie, J., Jaakkola, T.: Maximum margin matrix factorizations. In: Advances in Neural Information Processing Systems 17, pp. 1329–1336. MIT Press, Cambridge (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Roman Słowiński
    • 1
    • 2
  1. 1.Institute of Computing SciencePoznań University of TechnologyPoznańPoland
  2. 2.Systems Research InstitutePolish Academy of SciencesWarsawPoland

Personalised recommendations