Local and Global Approximations for Incomplete Data

  • Jerzy W. Grzymala-Busse
  • Wojciech Rzasa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4259)


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.


Incomplete Data Local Approximation Global Approximation None None Decision Table 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2006

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.Institute of MathematicsUniversity of RzeszowRzeszowPoland

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