A decision theoretic framework for approximating concepts
International Journal of Man-Machine Studies
Monotonicity and connectedness in learning systems
Monotonicity and connectedness in learning systems
Classification trees for problems with monotonicity constraints
ACM SIGKDD Explorations Newsletter
Rough sets and intelligent data analysis
Information Sciences—Informatics and Computer Science: An International Journal
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Developing and Testing Models for Replicating Credit Ratings: A Multicriteria Approach
Computational Economics
INFORMS Journal on Computing
Dominance-based rough set approach and knowledge reductions in incomplete ordered information system
Information Sciences: an International Journal
The investigation of the Bayesian rough set model
International Journal of Approximate Reasoning
Optimized generalized decision in dominance-based rough set approach
RSKT'07 Proceedings of the 2nd international conference on Rough sets and knowledge technology
Monotonic variable consistency rough set approaches
RSKT'07 Proceedings of the 2nd international conference on Rough sets and knowledge technology
Bayesian decision theory for dominance-based rough set approach
RSKT'07 Proceedings of the 2nd international conference on Rough sets and knowledge technology
Rough set approach to customer satisfaction analysis
RSCTC'06 Proceedings of the 5th international conference on Rough Sets and Current Trends in Computing
RSFDGrC'05 Proceedings of the 10th international conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing - Volume Part I
A measure of variance for hierarchical nominal attributes
Information Sciences: an International Journal
Rule learning with monotonicity constraints
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Learning Rule Ensembles for Ordinal Classification with Monotonicity Constraints
Fundamenta Informaticae - Fundamentals of Knowledge Technology
Dominance-based rough set approach to incomplete interval-valued information system
Data & Knowledge Engineering
Rough Set Approach to Knowledge Discovery about Preferences
ICCCI '09 Proceedings of the 1st International Conference on Computational Collective Intelligence. Semantic Web, Social Networks and Multiagent Systems
A Dominance-based Rough Set Approach to customer behavior in the airline market
Information Sciences: an International Journal
New applications and theoretical foundations of the dominance-based rough set approach
RSCTC'10 Proceedings of the 7th international conference on Rough sets and current trends in computing
Information Sciences: an International Journal
The Knowledge Engineering Review
A method for stochastic multiple criteria decision making based on dominance degrees
Information Sciences: an International Journal
The use of rough set methods in knowledge discovery in databases: tutorial abstract
RSFDGrC'11 Proceedings of the 13th international conference on Rough sets, fuzzy sets, data mining and granular computing
Learning monotone nonlinear models using the choquet integral
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part III
Attribute reduction in decision-theoretic rough set model: a further investigation
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
Dominance-based rough set model in intuitionistic fuzzy information systems
Knowledge-Based Systems
Learning partial ordinal class memberships with kernel-based proportional odds models
Computational Statistics & Data Analysis
Credit scoring analysis using a fuzzy probabilistic rough set model
Computational Statistics & Data Analysis
Bayesian rough set model: A further investigation
International Journal of Approximate Reasoning
An intuitionistic fuzzy dominance---based rough set
ICIC'11 Proceedings of the 7th international conference on Intelligent Computing: bio-inspired computing and applications
Fundamenta Informaticae - Advances in Rough Set Theory
Learning Rule Ensembles for Ordinal Classification with Monotonicity Constraints
Fundamenta Informaticae - Fundamentals of Knowledge Technology
Information Sciences: an International Journal
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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.