Lower and Upper Approximations in Data Tables Containing Possibilistic Information

  • Michinori Nakata
  • Hiroshi Sakai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4400)


An extended method of rough sets, called a method of weighted equivalence classes, is applied to a data table containing imprecise values expressed in a possibility distribution. An indiscerniblity degree between objects is calculated. A family of weighted equivalence classes is obtained via indiscernible classes from a binary relation for indiscernibility between objects. Each equivalence class in the family is accompanied by a possibilistic degree to which it is an actual one. By using the family of weighted equivalence classes we derive a lower approximation and an upper approximation. These approximations coincide with those obtained from methods of possible worlds. Therefore, the method of weighted equivalence classes is justified.


Rough sets Imprecise value Correctness criterion  Weighted equivalence class Lower and upper approximations 


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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Michinori Nakata
    • 1
  • Hiroshi Sakai
    • 2
  1. 1.Faculty of Management and Information Science, Josai International University, 1 Gumyo, Togane, Chiba, 283-8555Japan
  2. 2.Department of Mathematics and Computer Aided Sciences, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu, 804-8550Japan

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