Rough sets: probabilistic versus deterministic approach
International Journal of Man-Machine Studies
A decision-theoretic roguth set model
Methodologies for intelligent systems, 5
A decision theoretic framework for approximating concepts
International Journal of Man-Machine Studies
Variable precision rough set model
Journal of Computer and System Sciences
Relational interpretations of neighborhood operators and rough set approximation operators
Information Sciences—Informatics and Computer Science: An International Journal
Rules in incomplete information systems
Information Sciences: an International Journal
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
A Generalized Definition of Rough Approximations Based on Similarity
IEEE Transactions on Knowledge and Data Engineering
On the Extension of Rough Sets under Incomplete Information
RSFDGrC '99 Proceedings of the 7th International Workshop on New Directions in Rough Sets, Data Mining, and Granular-Soft Computing
Probabilistic approach to rough sets
International Journal of Approximate Reasoning
Decision-theoretic rough set models
RSKT'07 Proceedings of the 2nd international conference on Rough sets and knowledge technology
An empirical comparison of rule sets induced by LERS and probabilistic rough classification
RSCTC'10 Proceedings of the 7th international conference on Rough sets and current trends in computing
Generalized parameterized approximations
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
Definability and other properties of approximations for generalized indiscernibility relations
Transactions on Rough Sets XI
A New Version of the Rule Induction System LERS
Fundamenta Informaticae
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We study generalized probabilistic approximations, defined using both rough set theory and probability theory. The main objective is to study, for a given subset of the universe U, all such probabilistic approximations, i.e., for all parameter values. For an approximation space (U, R), where R is an equivalence relation, there is only one type of such probabilistic approximations. For an approximation space (U, R), where R is an arbitrary binary relation, three types of probabilistic approximations are introduced in this paper: singleton, subset and concept. We show that for a given concept the number of probabilistic approximations of given type is not greater than the cardinality of U. Additionally, we show that singleton probabilistic approximations are not useful for data mining, since such approximations, in general, are not even locally definable.