caa a22 4500 475799364 CHVBK 20180406123733.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1023/A:1008762812830 doi (NATIONALLICENCE)springer-10.1023/A:1008762812830 Consistency and Completeness in Rough Sets [Elektronische Daten] [Arul Siromoney, K. Inoue] 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. Kluwer Academic Publishers, 2000 knowledge discovery nationallicence machine learning nationallicence rough sets nationallicence inconsistency nationallicence Siromoney Arul School of Computer Science and Engineering, Anna University, 600 025, Chennai-, India aut Inoue K. Department of Computer Science and Systems Engineering, Faculty of Engineering, Yamaguchi University, 755-8611, Ube, Japan aut Journal of Intelligent Information Systems Kluwer Academic Publishers 15/3(2000-11-01), 207-220 0925-9902 15:3<207 2000 15 10844 https://doi.org/10.1023/A:1008762812830 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008762812830 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Siromoney Arul School of Computer Science and Engineering, Anna University, 600 025, Chennai-, India aut NATIONALLICENCE 700 1- Inoue K. Department of Computer Science and Systems Engineering, Faculty of Engineering, Yamaguchi University, 755-8611, Ube, Japan aut NATIONALLICENCE 773 0- Journal of Intelligent Information Systems Kluwer Academic Publishers 15/3(2000-11-01), 207-220 0925-9902 15:3<207 2000 15 10844 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer