Stochastic dominance-based rough set model for ordinal classification

W. Kotlowski, K. Dembczynski, Salvatore Greco, R. Slowinski

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)4019-4037
Number of pages19
JournalInformation Sciences
Issue number21
Publication statusPublished - 1 Nov 2008


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