Stochastic dominance-based rough set model for ordinal classification

• Published in: Information sciences Vol. 178; no. 21; pp. 4019 - 4037
• Main Authors: Kotłowski, Wojciech, Dembczyński, Krzysztof, Greco, Salvatore, Słowiński, Roman
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.11.2008
• Subjects: Dominance-based rough set approach; Empirical risk minimization; Isotonic regression; Maximum likelihood estimation; Monotonicity constraints; Multiple criteria decision analysis; Ordinal classification; Statistical decision theory; Variable consistency models; Maximum likelihood estimation; Variable consistency models; Empirical risk minimization; Isotonic regression; Multiple criteria decision analysis; Dominance-based rough set approach; Ordinal classification; Statistical decision theory; Monotonicity constraints
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2008.06.013

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.