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Local and Global Approximations for Incomplete Data

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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

For completely specified decision tables, where lower and upper approximations are unique, the lower approximation is the largest definable set contained in the approximated set X and the upper approximation of X is the smallest definable set containing X. For incomplete decision tables the existing definitions of upper approximations provide sets that, in general, are not minimal definable sets. The same is true for approximations based on relations that are generalizations of the equivalence relation. In this paper we introduce two definitions of approximations, local and global, such that the corresponding upper approximations are minimal. Local approximations are more precise than global approximations. Global lower approximations may be determined by a polynomial algorithm. However, algorithms to find both local approximations and global upper approximations are NP-hard.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, University of Kansas, Lawrence, KS, 66045, USA

    Jerzy W. Grzymala-Busse

  2. Institute of Computer Science, Polish Academy of Sciences, 01–237, Warsaw, Poland

    Jerzy W. Grzymala-Busse

  3. Institute of Mathematics, University of Rzeszow, 35–310, Rzeszow, Poland

    Wojciech Rzasa

Authors
  1. Jerzy W. Grzymala-Busse
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  2. Wojciech Rzasa
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Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco

  2. Graduate School of Engineering, Department of Electrical Engineering and Computer Sciences, University of Hyogo, 2167 Shosha, 671-2280,, Himeji, Hyogo, Japan

    Yutaka Hata

  3. Department of Medical Informatics, Faculty of Medicine, Shimane University, 89-1 Enya-cho, Izumo, 693-8501, Shimane, Japan

    Shoji Hirano

  4. Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama, Toyonaka, 560-8531, Osaka, Japan

    Masahiro Inuiguchi

  5. Department of Risk Engineering, School of Systems and Information Engineering, University of Tsukuba, 305-8573, Ibaraki, Japan

    Sadaaki Miyamoto

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

    Hung Son Nguyen

  7. Systems Research Institute, Polish Academy of Sciences, 01-447, Warsaw, Poland

    Roman Słowiński

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© 2006 Springer-Verlag Berlin Heidelberg

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Grzymala-Busse, J.W., Rzasa, W. (2006). Local and Global Approximations for Incomplete Data. 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_27

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  • DOI: https://doi.org/10.1007/11908029_27

  • 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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