Abstract
When arbitrary sets are approximated by more structured sets, it may not be possible to obtain an exact approximation that is equivalent to a given set. A proposal is presented for a ‘metric’ approach to Rough Sets. This includes a definition of the ‘optimal’ or best approximation with respect to a measure of similarity, and an algorithm to find it using the Jaccard Index. A definition of consistency also allows the algorithm to work for a larger class of similarity measures. Several consequences of these definitions are also presented.
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Janicki, R., Lenarčič, A. (2013). Optimal Approximations with Rough Sets. In: Lingras, P., Wolski, M., Cornelis, C., Mitra, S., Wasilewski, P. (eds) Rough Sets and Knowledge Technology. RSKT 2013. Lecture Notes in Computer Science(), vol 8171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41299-8_9
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DOI: https://doi.org/10.1007/978-3-642-41299-8_9
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