Abstract
We generalize the standard rough set pair induced by an equivalence E on U in such a way that the upper approximation defined by E is replaced by the upper approximations determined by tolerances \(T_{1},\ldots ,T_{n}\) on U. Using this kind of multiple upper approximations we can express “softer” uncertainties of different kinds. We can order the set \( RS (E,T_{1},\ldots ,T_{n})\) of the multiple approximations of all subsets of the universe U by the coordinatewise inclusion. We show that whenever the tolerances \(T_{1},\ldots ,T_{n}\) are E-compatible, this ordered set forms a complete lattice. As a special case we show how this complete lattice can be reduced to the complete lattice of the traditional rough sets defined by the equivalence E.
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Järvinen, J., Kovács, L., Radeleczki, S. (2019). Rough Sets Defined by Multiple Relations. In: Mihálydeák, T., et al. Rough Sets. IJCRS 2019. Lecture Notes in Computer Science(), vol 11499. Springer, Cham. https://doi.org/10.1007/978-3-030-22815-6_4
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DOI: https://doi.org/10.1007/978-3-030-22815-6_4
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