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Algebras from Rough Sets

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Rough-Neural Computing

Part of the book series: Cognitive Technologies ((COGTECH))

Summary

Rough set theory has seen nearly two decades of research on both foundations and on diverse applications. A substantial part of the work done on the theory has been devoted to the study of its algebraic aspects. ‘Rough algebras’ now abound, and have been shown to be instances of various algebraic structures, both well-established and relatively new, e.g., quasi-Boolean, Stone, double Stone, Nelson, Lukasiewicz algebras, on the one hand, and topological quasi-Boolean, prerough and rough algebras, on the other. More interestingly and importantly, some of these latter algebras find a new dimension (interpretation) through representations as rough structures. An attempt is made here to present the various relationships and to discuss the representation results.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Kanpur, 208 016, India

    Mohua Banerjee

  2. Department of Pure Mathematics, University of Kolkata, 35, Ballygunge Circular Road, Kolkata, 700019, India

    Mihir K. Chakraborty

Authors
  1. Mohua Banerjee
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  2. Mihir K. Chakraborty
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Editor information

Editors and Affiliations

  1. Indian Statistical Institute, Machine Intelligence Unit, 203 Barrackpore Trunk Road, Calcutta, 700 035, India

    Sankar K. Pal

  2. Department of Mathematics and Computer Science, University of Warmia and Mazury, Zolnierska 14, Olsztyn, Poland

    Lech Polkowski

  3. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

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Banerjee, M., Chakraborty, M.K. (2004). Algebras from Rough Sets. In: Pal, S.K., Polkowski, L., Skowron, A. (eds) Rough-Neural Computing. Cognitive Technologies. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18859-6_7

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  • DOI: https://doi.org/10.1007/978-3-642-18859-6_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-62328-8

  • Online ISBN: 978-3-642-18859-6

  • eBook Packages: Springer Book Archive

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