Abstract
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.
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Keywords
- Decision Table
- Approximation Space
- Indiscernibility Relation
- Incomplete Information System
- Arbitrary Binary Relation
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Grzymała-Busse, J.W. (2011). Generalized Parameterized Approximations. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds) Rough Sets and Knowledge Technology. RSKT 2011. Lecture Notes in Computer Science(), vol 6954. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24425-4_20
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DOI: https://doi.org/10.1007/978-3-642-24425-4_20
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