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Categorical Innovations for Rough Sets

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Rough Set Theory: A True Landmark in Data Analysis

Part of the book series: Studies in Computational Intelligence ((SCI,volume 174))

Summary

Categories arise in mathematics and appear frequently in computer science where algebraic and logical notions have powerful representations using categorical constructions. In this chapter we lean towards the functorial view involving natural transformations and monads. Functors extendable to monads, further incorporating order structure related to the underlying functor, turn out to be very useful when presenting rough sets beyond relational structures in the usual sense. Relations can be generalized with rough set operators largely maintaining power and properties. In this chapter we set forward our required categorical tools and we show how rough sets and indeed a theory of rough monads can be developed. These rough monads reveal some canonic structures, and are further shown to be useful in real applications as well. Information within pharmacological treatment can be structured by rough set approaches. In particular, situations involving management of drug interactions and medical diagnosis can be described and formalized using rough monads.

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Author information

Authors and Affiliations

  1. Department of Computing Science, Umeå University, Sweden

    P. Eklund

  2. Department of Applied Mathematics, University of Málaga, Spain

    M. A. Galán

  3. Department of Computer Architecture, University of Málaga, Spain

    J. Karlsson

Authors
  1. P. Eklund
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  2. M. A. Galán
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  3. J. Karlsson
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Editor information

Editors and Affiliations

  1. Norwegian University of Science and Technology, Trondheim, Norway

    Ajith Abraham

  2. School of Information Technology and Engineering (SITE), Central University of Las Villas, Villa Clara, Cuba

    Rafael Falcón

  3. Department of Computer Science, Central University of LasVillas, 54830, Villa Clara, Cuba

    Rafael Bello

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Eklund, P., Galán, M.A., Karlsson, J. (2009). Categorical Innovations for Rough Sets. In: Abraham, A., Falcón, R., Bello, R. (eds) Rough Set Theory: A True Landmark in Data Analysis. Studies in Computational Intelligence, vol 174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89921-1_2

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  • DOI: https://doi.org/10.1007/978-3-540-89921-1_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89920-4

  • Online ISBN: 978-3-540-89921-1

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