Quality of Rough Approximation in Multi-criteria Classification Problems

  • Krzysztof Dembczyński
  • Salvatore Greco
  • Wojciech Kotłowski
  • Roman Słowiński
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4259)


Dominance-based Rough Set Approach (DRSA) has been proposed to deal with multi-criteria classification problems, where data may be inconsistent with respect to the dominance principle. In this paper, we consider different measures of the quality of approximation, which is the value indicating how much inconsistent the decision table is. We begin with the classical definition, based on the relative number of inconsistent objects. Since this measure appears to be too restrictive in some cases, a new approach based on the concept of generalized decision is proposed. Finally, motivated by emerging problems in the presence of noisy data, the third measure based on the object reassignment is introduced. Properties of these measures are analysed in light of rough set theory.


Reference Object Decision Table Class Assignment Decision Class Inconsistent Object 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Krzysztof Dembczyński
    • 1
  • Salvatore Greco
    • 2
  • Wojciech Kotłowski
    • 1
  • Roman Słowiński
    • 1
    • 3
  1. 1.Institute of Computing SciencePoznań University of TechnologyPoznańPoland
  2. 2.Faculty of EconomicsUniversity of CataniaCataniaItaly
  3. 3.Institute for Systems ResearchPolish Academy of SciencesWarsawPoland

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