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

  • Authors:
  • Hiroshi Sakai;Ryuji Ishibashi;Michinori Nakata

  • Affiliations:
  • Mathematical Sciences Section, Department of Basic Sciences Faculty of Engineering, Kyushu Institute of Technology, Tobata, Japan 804;Mathematical Sciences Section, Department of Basic Sciences Faculty of Engineering, Kyushu Institute of Technology, Tobata, Japan 804;Faculty of Management and Information Science, Josai International University, Gumyo, Togane, Japan

  • Venue:
  • RSCTC '08 Proceedings of the 6th International Conference on Rough Sets and Current Trends in Computing
  • Year:
  • 2008

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Abstract

A rule in a DeterministicInformationSystem(DIS) is often defined by an implicationτsuch that both support(τ) ≥αand accuracy(τ) ≥βhold for the threshold values ¿andß. In a Non-deterministicInformationSystem(NIS), there arederivedDISsdue to the informationincompleteness. The definition of a rule in a DISisextended to the lowerand upperapproximationsof a rule in a NIS. Thisdefinition explicitly handles non-deterministic information andincomplete information. To implement the utility programs for twoapproximations, Apriorialgorithm is extended. Even thoughthe number of derived DISsincreases in exponential order,this extended algorithm does not depend upon the number of derivedDISs. A prototype system is implemented, and this systemis applied to some data sets.