Abstract
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.
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Grzymala-Busse, J.W. (2013). Generalized Probabilistic Approximations. In: Peters, J.F., Skowron, A., Ramanna, S., Suraj, Z., Wang, X. (eds) Transactions on Rough Sets XVI. Lecture Notes in Computer Science, vol 7736. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36505-8_1
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DOI: https://doi.org/10.1007/978-3-642-36505-8_1
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