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λ-Connected Approximations for Rough Sets

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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

Rough sets was first studied by Pawlak to describe the approximation of a set X by using its lower bound L(X) and upper bound U(X). λ-connectedness was originally proposed as a technique to search layers in 2D or 3D digital seismic data. This note introduces λ-connected components to represent lower and upper approximations for rough sets. According to Pawlak’s definition of the boundary of X, BN(X) = U(X)-L(X), U(X) contains two “layers:” L(X) and BN(X). Representing the “layer” of BN(X) is one of the key problems in rough set theory. This note shows when the boundary of X contains the property of gradual variations, BN(X) can be represented by a partition of λ-connectedness which is a generalization of α-cut representation.

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Author information

Authors and Affiliations

  1. University of The District of Columbia, Washington, DC, 20008, USA

    Li Chen

Authors
  1. Li Chen
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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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Chen, L. (2002). λ-Connected Approximations for Rough Sets. 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_76

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  • DOI: https://doi.org/10.1007/3-540-45813-1_76

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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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