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Monads Can Be Rough

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Rough Sets and Current Trends in Computing (RSCTC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4259))

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Abstract

Traditionally, rough sets build upon relations based on ordinary sets, i.e. relations on X as subsets of X×X. A starting point of this paper is the equivalent view on relations as mappings from X to the (ordinary) power set PX. Categorically, P is a set functor, and even more so, it can in fact be extended to a monad (P,η,μ). This is still not enough and we need to consider the partial order (PX,≤). Given this partial order, the ordinary power set monad can be extended to a partially ordered monad. The partially ordered ordinary power set monad turns out to contain sufficient structure in order to provide rough set operations. However, the motivation of this paper goes far beyond ordinary relations as we show how more general power sets, i.e. partially ordered monads built upon a wide range of set functors, can be used to provide what we call rough monads.

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© 2006 Springer-Verlag Berlin Heidelberg

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Eklund, P., Galán, M.A. (2006). Monads Can Be Rough. In: Greco, S., et al. Rough Sets and Current Trends in Computing. RSCTC 2006. Lecture Notes in Computer Science(), vol 4259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11908029_9

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  • DOI: https://doi.org/10.1007/11908029_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-47693-1

  • Online ISBN: 978-3-540-49842-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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