In this paper we analyze the basic concepts of rough set theory, lower and upper approximations, defined in an approximation space \((U,\textbf{L})\), where U is a nonempty and finite set and L is a fixed family of subsets of U. Some definitions of such lower and upper approximations are well known, some are presented in this paper for the first time. Our new definitions better accommodate applications to mining incomplete data, i.e., data with missing attribute values. An illustrative example is also presented in this paper.


Lower Approximation Local Approximation Decision Table Approximation Space Dual Approximation 
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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jerzy W. Grzymala-Busse
    • 1
    • 2
  • Wojciech Rzasa
    • 3
  1. 1.Department of Electrical Engineering and Computer ScienceUniversity of KansasLawrenceUSA
  2. 2.Institute of Computer SciencePolish Academy of SciencesWarsawPoland
  3. 3.Department of Computer ScienceUniversity of RzeszowRzeszówPoland

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