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International Conference on Rough Sets and Current Trends in Computing

RSCTC 2008: Rough Sets and Current Trends in Computing pp 299–309Cite as

Lower and Upper Approximations of Rules in Non-deterministic Information Systems

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5306))

Abstract

A rule in a Deterministic Information System (DIS) is often defined by an implication τ such that both support(τ) ≥ α and accuracy(τ) ≥ β hold for the threshold values α and β. In a Non-deterministic Information System (NIS), there are derived DISs due to the information incompleteness. The definition of a rule in a DIS is extended to the lower and upper approximations of a rule in a NIS. This definition explicitly handles non-deterministic information and incomplete information. To implement the utility programs for two approximations, Apriori algorithm is extended. Even though the number of derived DISs increases in exponential order, this extended algorithm does not depend upon the number of derived DISs. A prototype system is implemented, and this system is applied to some data sets.

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Author information

Authors and Affiliations

  1. Mathematical Sciences Section, Department of Basic Sciences Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu, 804, Japan

    Hiroshi Sakai & Ryuji Ishibashi

  2. Faculty of Management and Information Science, Josai International University, Gumyo, Togane, Chiba 283, Japan

    Michinori Nakata

Authors
  1. Hiroshi Sakai
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  2. Ryuji Ishibashi
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  3. Michinori Nakata
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Editor information

Editors and Affiliations

  1. Department of Computer Science, The University of Akron, OH 44325-4003, Akron, USA

    Chien-Chung Chan

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

    Jerzy W. Grzymala-Busse

  3. Department of Computer Science, University of Regina,, S4S 0A2, Regina, Saskatchewan, Canada

    Wojciech P. Ziarko

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Sakai, H., Ishibashi, R., Nakata, M. (2008). Lower and Upper Approximations of Rules in Non-deterministic Information Systems. In: Chan, CC., Grzymala-Busse, J.W., Ziarko, W.P. (eds) Rough Sets and Current Trends in Computing. RSCTC 2008. Lecture Notes in Computer Science(), vol 5306. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88425-5_31

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  • DOI: https://doi.org/10.1007/978-3-540-88425-5_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88423-1

  • Online ISBN: 978-3-540-88425-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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