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On Asymptotic Properties of Rough— Set— Theoretic Approximations. Fractal Dimension, Exact Sets, and Rough Inclusion in Potentially Infinite Information Systems

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Book cover Rough Sets and Current Trends in Computing (RSCTC 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2475))

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Abstract

We look at asymptotic properties of rough set approximations exploiting them to three-fold purpose viz. to introduce a counterpart of fractal dimension in abstract information systems, to define the notion of an exact set in infinite information system to the result that so defined exact sets form a compact metric Boolean algebra of sets, and to introduce rough inclusion measures for rough mereology for infinitary concepts.

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Author information

Authors and Affiliations

  1. Polish-Japanese Institute of Information Technology, Koszykowa 86, 02-008, Warsaw, Poland

    Lech Polkowski

  2. Department of Mathematics and Computer Science, University of Warmia and Mazury, Zolnierska 14, Olsztyn, 10 670, Poland

    Lech Polkowski

Authors
  1. Lech Polkowski
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Editor information

Editors and Affiliations

  1. Penn State Great Valley School of Professional Graduate Studies, 30 East Swedesford Road, Malvern, PA, 19355, USA

    James J. Alpigini

  2. Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canada

    James F. Peters

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

    Andrzej Skowron

  4. Department of Systems and Information Engineering, Maebashi Institute of Technology, 460-1 Kamisadori-Cho, Maebashi-City, 371-0816, Japan

    Ning Zhong

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© 2002 Springer-Verlag Berlin Heidelberg

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Polkowski, L. (2002). On Asymptotic Properties of Rough— Set— Theoretic Approximations. Fractal Dimension, Exact Sets, and Rough Inclusion in Potentially Infinite Information Systems. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds) Rough Sets and Current Trends in Computing. RSCTC 2002. Lecture Notes in Computer Science(), vol 2475. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45813-1_21

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  • DOI: https://doi.org/10.1007/3-540-45813-1_21

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44274-5

  • Online ISBN: 978-3-540-45813-5

  • eBook Packages: Springer Book Archive

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