An Equivalent Definition of Rough Sets

  • Guilong Liu
  • James Kuodo Huang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5306)


Using characteristic function of sets, this paper proposes the concept of linear mappings for the power sets of universal sets. Through this concept, we explain rough set upper approximation as a linear mapping and study the linear properties of rough sets. The relationship between the linear mappings and the upper approximations is established. The results and methods given in this paper will hopefully simplify the theoretical and practical researches of rough sets.


Rough sets Binary relations Approximations Composition of relations Characteristic functions 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Guilong Liu
    • 1
  • James Kuodo Huang
    • 2
  1. 1.School of Information ScienceBeijing Language and Culture UniversityBeijingChina
  2. 2.Association of International Uncertainty ComputingAlhambraUSA

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