Quality of rough approximation in multi-criteria classification problems

Authors:
Krzysztof Dembczyński;Salvatore Greco;Wojciech Kotłowski;Roman Słowiński
Affiliations:
Institute of Computing Science, Poznań University of Technology, Poznań, Poland;Faculty of Economics, University of Catania, Catania, Italy;Institute of Computing Science, Poznań University of Technology, Poznań, Poland;Institute of Computing Science, Poznań University of Technology, Poznań, Poland
Venue:
RSCTC'06 Proceedings of the 5th international conference on Rough Sets and Current Trends in Computing
Year:
2006

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Abstract

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.