Consistency and Completeness in Rough Sets

  • Authors:

  • Arul Siromoney;K. Inoue

  • Affiliations:

  • School of Computer Science and Engineering, Anna University, Chennai-600 025, India. asiro@vsnl.com;Department of Computer Science and Systems Engineering, Faculty of Engineering, Yamaguchi University, Ube 755-8611, Japan. inoue@csse.yamaguchi-u.ac.jp

  • Venue:
  • Journal of Intelligent Information Systems
  • Year:
  • 2000

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Abstract

Consistency and completeness are defined in the context of rough set theory and shown to be related to the lower approximation and upper approximation, respectively. A member of a composed set (union of elementary sets) that is consistent with respect to a concept, surely belongs to the concept. An element that is not a member of a composed set that is complete with respect to a concept, surely does not belong to the concept. A consistent rule and a complete rule are useful in addition to any other rules learnt to describe a concept. When an element satisfies the consistent rule, it surely belongs to the concept, and when it does not satisfy the complete rule, it surely does not belong to the concept. In other cases, the other learnt rules are used. The results in the finite universe are extended to the infinite universe, thus introducing a rough set model for the learning from examples paradigm. The results in this paper have application in knowledge discovery or learning from database environments that are inconsistent, but at the same time demand accurate and definite knowledge. This study of consistency and completeness in rough sets also lays the foundation for related work at the intersection of rough set theory and inductive logic programming.