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
Definability and other properties of approximations for generalized indiscernibility relations
Transactions on Rough Sets XI
Local probabilistic approximations for incomplete data
ISMIS'12 Proceedings of the 20th international conference on Foundations of Intelligent Systems
Generalized probabilistic approximations
Transactions on Rough Sets XVI
Generalized probabilistic approximations of incomplete data
International Journal of Approximate Reasoning
An Experimental Comparison of Three Probabilistic Approximations Used for Rule Induction
Fundamenta Informaticae - To Andrzej Skowron on His 70th Birthday
Unifying Rough Set Theories via Large Scaled Granular Computing
Fundamenta Informaticae - To Andrzej Skowron on His 70th Birthday
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We study generalized parameterized 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 parameterized 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 parameterized approximations. For an approximation space (U,R), where R is an arbitrary binary relation, three types of parameterized approximations are introduced in this paper: singleton, subset and concept. We show that the number of parameterized approximations of given type is not greater than the cardinality of U. Additionally, we show that singleton parameterized approximations are not useful for data mining, since such approximations, in general, are not even locally definable.