Stochastic dominance-based rough set model for ordinal classification

  • Authors:
  • Wojciech Kotłowski;Krzysztof Dembczyński;Salvatore Greco;Roman Słowiński

  • Affiliations:
  • Institute of Computing Science, Poznań University of Technology, Piotrowo 2, Poznań 60-965, Poland;Institute of Computing Science, Poznań University of Technology, Piotrowo 2, Poznań 60-965, Poland;Faculty of Economics, University of Catania, 95129 Catania, Italy;Institute of Computing Science, Poznań University of Technology, Piotrowo 2, Poznań 60-965, Poland and Institute for Systems Research, Polish Academy of Sciences, Warsaw 01-447, Poland

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2008

Quantified Score

Hi-index 0.07

Visualization

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 ordinal classification with monotonicity constraints (also referred to as multicriteria classification in decision analysis). However, in real-life problems, in the presence of noise, the notions of rough approximations were found to be excessively restrictive. In this paper, we introduce a probabilistic model for ordinal classification problems with monotonicity constraints. Then, we generalize the notion of lower approximations to the stochastic case. We estimate the probabilities with the maximum likelihood method which leads to the isotonic regression problem for a two-class (binary) case. The approach is easily generalized to a multi-class case. Finally, we show the equivalence of the variable consistency rough sets to the specific empirical risk-minimizing decision rule in the statistical decision theory.