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Dominance-Based Rough Set Approach to Multiple Criteria Ranking with Sorting-Specific Preference Information

  • Miłosz Kadziński
  • Roman Słowiński
  • Marcin Szeląg
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 605)

Abstract

A novel multiple criteria decision aiding method is proposed, that delivers a recommendation characteristic for ranking problems but employs preference information typical for sorting problems. The method belongs to the category of ordinal regression methods: it starts with preference information provided by the Decision Maker (DM) in terms of decision examples, and then builds a preference model that reproduces these exemplary decisions. The ordinal regression is analogous to inductive learning of a model that is true in the closed world of data where it comes from. The sorting examples show an assignment of some alternatives to pre-defined and ordered quality classes. Although this preference information is purely ordinal, the number of quality classes separating two assigned alternatives is meaningful for an ordinal intensity of preference. Using an adaptation of the Dominance-based Rough Set Approach (DRSA), the method builds from this information a decision rule preference model. This model is then applied on a considered set of alternatives to finally rank them from the best to the worst. The decision rule preference model resulting from DRSA is able to represent the preference information about the ordinal intensity of preference without converting this information into a cardinal scale. Moreover, the decision rules can be interpreted straightforwardly by the DM, facilitating her understanding of the feedback between the preference information and the preference model. An illustrative case study performed in this paper supports this claim.

Keywords

Decision analysis Preference learning Ranking Dominance-based rough set approach Decision rules Assignment examples 

Notes

Acknowledgments

The first author acknowledges financial support from the National Science Center (grant no. DEC-2013/11/D/ST6/03056). The third author declares that he is a scholarship holder within the 2012/2013 project “Scholarship support for Ph.D. students specializing in majors strategic for Wielkopolska’s development”, Sub-measure 8.2.2 of Human Capital Operational Programme, co-financed by European Union under the European Social Fund.

References

  1. 1.
    Bana e Costa CA, Vansnick J-C (1994) MACBETH: an interactive path towards the construction of cardinal value functions. Int Trans Oper Res 1(4):387–500Google Scholar
  2. 2.
    Błaszczyński J, Słowiński R, Szeląg M (2010) Probabilistic rough set approaches to ordinal classification with monotonicity constraints. In: Hüllermeier E, Kruse R, Hoffmann F (eds) IPMU 2010. Lecture notes in artificial intelligence, vol 6178. Springer, Berlin, pp 99–108Google Scholar
  3. 3.
    Błaszczyński J, Słowiński R, Szeląg M (2011) Sequential covering rule induction algorithm for variable consistency rough set approaches. Inf Sci 181:987–1002Google Scholar
  4. 4.
    Corrente S, Greco S, Kadziński M, Słowiński R (2013) Robust ordinal regression in preference learning and ranking. Mach Learn 93:381–422MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Dembczyński K, Kotłowski W, Słowiński R, Szeląg M (2010) Learning of rule ensembles for multiple attribute ranking problems. In: Fürnkranz J, Hüllermeier E (eds) Preference learning. Springer, Berlin, pp 217–247Google Scholar
  6. 6.
    Doumpos M, Zopounidis C (2012) Preference disaggregation and statistical learning for multicriteria decision support: a review. Eur J Oper Res 209(3):203–214MathSciNetCrossRefGoogle Scholar
  7. 7.
    Figueira J, Greco S, Słowiński R (2009) Building a set of additive value functions representing a reference preorder and intensities of preference: grip method. Eur J Oper Res 195(2):460–486CrossRefGoogle Scholar
  8. 8.
    Fortemps P, Greco S, Słowiński R (2008) Multicriteria decision support using rules that represent rough-graded preference relations. Eur J Oper Res 188(1):206–223CrossRefMATHGoogle Scholar
  9. 9.
    Fürnkranz J, Hüllermeier E (2003) Pairwise preference learning and ranking. In: Lavrac N, Gamberger D, Todorovski L, Blockeel H (eds) Proceedings of the European conference on machine learning (ECML 2003). Lecture notes in artificial intelligence, vol 2837. Springer, pp 145–156Google Scholar
  10. 10.
    Fürnkranz J, Hüllermeier E (eds) (2010) Preference learning. Springer, BerlinGoogle Scholar
  11. 11.
    Greco S, Matarazzo B, Słowiński R (1999) Rough approximation of a preference relation by dominance relations. Eur J Oper Res 117:63–83CrossRefMATHGoogle Scholar
  12. 12.
    Greco S, Matarazzo B, Słowiński R (2001) Rough sets theory for multicriteria decision analysis. Eur J Oper Res 129(1):1–47CrossRefGoogle Scholar
  13. 13.
    Greco S, Matarazzo B, Słowiński R (2005) Decision rule approach. In: Figueira J, Greco S, Ehrgott M (eds) Multiple criteria decision analysis: state of the art surveys. Chap. 13. Springer, New York, pp 507–562Google Scholar
  14. 14.
    Greco S, Matarazzo B, Słowiński R (2005) Preference representation by means of conjoint measurement and 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. Kluwer, Boston, pp 263–313Google Scholar
  15. 15.
    Greco S, Matarazzo B, Słowiński R, Stefanowski J (2001) An algorithm for induction of decision rules consistent with the dominance principle. In: Ziarko W, Yao YY (eds) Rough sets and current trends in computing 2001. Lecture notes in artificial intelligence, vol 2005. Springer, Berlin, pp 304–313Google Scholar
  16. 16.
    Grzymała-Busse JW (1992) LERS—a system for learning from examples based on rough sets. In: Słowiński R (ed) Intelligent decision support. Handbook of Applications and Advances of the Rough Sets Theory. Kluwer, Dordrecht, pp 3–18Google Scholar
  17. 17.
    Grzymała-Busse JW (1997) A new version of the rule induction system LERS. Fundamenta Informaticae 31(1):27–39MATHGoogle Scholar
  18. 18.
    Liu T-Y (2011) Learning to rank for information retrieval. Springer, BerlinCrossRefMATHGoogle Scholar
  19. 19.
    Roy B, Słowiński R (2013) Questions guiding the choice of a multicriteria decision aiding method. EURO J Decis Process 1(1):69–97CrossRefGoogle Scholar
  20. 20.
    Saaty T (1980) The analytic hierarchy process. McGraw Hill, New YorkMATHGoogle Scholar
  21. 21.
    Słowiński R, Greco S, Matarazzo B (2009) Rough sets in decision making. In: Meyers RA (ed) Encyclopedia of complexity and systems science. Springer, New York, pp 7753–7786Google Scholar
  22. 22.
    Słowiński R, Greco R, Matarazzo B (2014) Rough set based decision support. In: Burke EK, Kendall G (eds) Search methodologies: introductory tutorials in optimization and decision support techniques, Chap. 19, 2nd edn. Springer, New York, pp 557–609Google Scholar
  23. 23.
    Stefanowski J (2001) Algorytmy indukcji reguł decyzyjnych w odkrywaniu wiedzy. Rozprawy, vol 361. Wydawnictwo Politechniki PoznańskiejGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Miłosz Kadziński
    • 1
  • Roman Słowiński
    • 1
    • 2
  • Marcin Szeląg
    • 1
  1. 1.Institute of Computing SciencePoznań University of TechnologyPoznańPoland
  2. 2.Systems Research Institute, Polish Academy of SciencesWarsawPoland

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