Journal
INFORMATION SCIENCES
Volume 178, Issue 21, Pages 4019-4037Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ins.2008.06.013
Keywords
dominance-based rough set approach; ordinal classification; monotonicity constraints; isatanic regression; maximum likelihood estimation; variable consistency models; statistical decision theory; empirical risk minimization; multiple criteria decision analysis
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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. (C) 2008 Elsevier Inc. All rights reserved.
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