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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Generalized Parameterized Approximations
verfasst von : Jerzy W. Grzymała-Busse
Erschienen in: Rough Sets and Knowledge Technology
Verlag: Springer Berlin Heidelberg
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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.