Rules and Apriori Algorithm in Non-deterministic Information Systems

  • Authors:

  • Hiroshi Sakai;Ryuji Ishibashi;Kazuhiro Koba;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;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 283

  • Venue:
  • Transactions on Rough Sets IX
  • Year:
  • 2008

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Abstract

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.