Statistical Model for Rough Set Approach to Multicriteria Classification

Authors:
Krzysztof Dembczyński;Salvatore Greco;Wojciech Kotłowski;Roman Słowiński
Affiliations:
Institute of Computing Science, Poznań University of Technology, 60-965 Poznań, Poland,;Faculty of Economics, University of Catania, 95129 Catania, Italy,;Institute of Computing Science, Poznań University of Technology, 60-965 Poznań, Poland,;Institute of Computing Science, Poznań University of Technology, 60-965 Poznań, Poland, and Institute for Systems Research, Polish Academy of Sciences, 01-447 Warsaw, Poland,
Venue:
PKDD 2007 Proceedings of the 11th European conference on Principles and Practice of Knowledge Discovery in Databases
Year:
2007

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Abstract

In order to discover interesting patterns and dependencies in data, an approach based on rough set theory can be used. In particular, Dominance-based Rough Set Approach (DRSA) has been introduced to deal with the problem of multicriteria classification. However, in real-life problems, in the presence of noise, the notions of rough approximations were found to be excessively restrictive, which led to the proposal of the Variable Consistency variant of DRSA. In this paper, we introduce a new approach to variable consistency that is based on maximum likelihood estimation. For two-class (binary) problems, it leads to the isotonic regression problem. The approach is easily generalized for the multi-class case. Finally, we show the equivalence of the variable consistency rough sets to the specific risk-minimizing decision rule in statistical decision theory.