Rules and Apriori Algorithm in Non-deterministic Information Systems

  • Hiroshi Sakai
  • Ryuji Ishibashi
  • Kazuhiro Koba
  • Michinori Nakata
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5390)


This paper presents a framework of rule generation in Non-deterministic Information Systems (NISs), which follows rough sets based rule generation in Deterministic Information Systems (DISs). Our previous work about NISs coped with certain rules, minimal certain rules and possible rules. These rules are characterized by the concept of consistency. This paper relates possible rules to rules by the criteria support and accuracy in NISs. On the basis of the information incompleteness in NISs, it is possible to define new criteria, i.e., minimum support, maximum support, minimum accuracy and maximum accuracy. Then, two strategies of rule generation are proposed based on these criteria. The first strategy is Lower Approximation strategy, which defines rule generation under the worst condition. The second strategy is Upper Approximation strategy, which defines rule generation under the best condition. To implement these strategies, we extend Apriori algorithm in DISs to Apriori algorithm in NISs. A prototype system is implemented, and this system is applied to some data sets with incomplete information.


Rough sets Non-deterministic information Incomplete information Rule generation Lower and upper approximations Apriori algorithm 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hiroshi Sakai
    • 1
  • Ryuji Ishibashi
    • 1
  • Kazuhiro Koba
    • 1
  • Michinori Nakata
    • 2
  1. 1.Mathematical Sciences Section, Department of Basic Sciences, Faculty of EngineeringKyushu Institute of TechnologyTobataJapan
  2. 2.Faculty of Management and Information ScienceJosai International UniversityGumyo, ToganeJapan

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