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Transactions on Rough Sets VIII pp 21–34Cite as

Local and Global Approximations for Incomplete Data

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Part of the book series: Lecture Notes in Computer Science ((TRS,volume 5084))

Abstract

For completely specified decision tables 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 generalizations of approximations based on relations that are not equivalence relations. 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. Additionally, we show that for decision tables with all missing attribute values being lost, local and global approximations are equal to one another and that they are unique.

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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. Grzymała-Busse

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

    Jerzy W. Grzymała-Busse

  3. Department of Computer Science, University of Rzeszow, 35–310, Rzeszow, Poland

    Wojciech Rza̧sa

Authors
  1. Jerzy W. Grzymała-Busse
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  2. Wojciech Rza̧sa
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James F. Peters Andrzej Skowron

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Grzymała-Busse, J.W., Rza̧sa, W. (2008). Local and Global Approximations for Incomplete Data. In: Peters, J.F., Skowron, A. (eds) Transactions on Rough Sets VIII. Lecture Notes in Computer Science, vol 5084. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85064-9_2

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  • DOI: https://doi.org/10.1007/978-3-540-85064-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85063-2

  • Online ISBN: 978-3-540-85064-9

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